Leonard Carlitz

Q: What Schools Are Affiliated With Leonard Carlitz

Leonard Carlitz is affiliated with the following schools: California Institute of Technology, University of Chicago, Duke University, University of Cambridge, University of Pennsylvania

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Leonard Carlitz

Mathematics

#986

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#1702

Historical Rank

#430

USA Rank

Measure Theory

#39

World Rank

#68

Historical Rank

#22

USA Rank

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Mathematics

Leonard Carlitz's Degrees

PhD Mathematics University of Chicago

Why Is Leonard Carlitz Influential?

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According to Wikipedia, Leonard Carlitz was an American mathematician. Carlitz supervised 44 doctorates at Duke University and published over 770 papers. Chronology 1907 Born Philadelphia, PA, USA1927 BA, University of Pennsylvania1930 PhD, University of Pennsylvania, 1930 under Howard Mitchell, who had studied under Oswald Veblen at Princeton1930–31 at Caltech with E. T. Bell1931 married Clara Skaler1931–32 at Cambridge with G. H. Hardy1932 Joined the faculty of Duke University where he served for 45 years1938 to 1973 Editorial Board Duke Mathematical Journal 1939 Birth of son Michael1940 Supervision of his first doctoral student E. F. Canaday, awarded 19401945 Birth of son Robert1964 First James B. Duke Professor in Mathematics1977 Supervised his 44th and last doctoral student, Jo Ann Lutz, awarded 19771977 Retired1990 Death of wife Clara, after 59 years of marriage1999 September 17 Died in Pittsburgh, PA

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Leonard Carlitz's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

$q$-Bernoulli numbers and polynomials (1948) (325)
On certain functions connected with polynomials in a Galois field (1935) (313)
$q$-Bernoulli and Eulerian numbers (1954) (286)
Eulerian Numbers and Polynomials (1959) (195)
Some Orthogonal q‐Polynomials (1965) (176)
A degenerate Staudt-Clausen theorem (1956) (161)
A Combinatorial Property of q-Eulerian Numbers (1975) (154)
A CHARACTERIZATION OF ALGEBRAIC NUMBER FIELDS WITH CLASS NUMBER TWO (1960) (134)
Two element lattice permutation numbers and their $q$-generalization (1964) (113)
Arithmetic Properties of Generalized Bernoulli Numbers. (1959) (107)
Some theorems on generalized Dedekind sums (1953) (101)
Bounds for exponential sums (1957) (99)
A class of polynomials (1938) (94)
Explicit evaluation of certain exponential sums. (1979) (88)
Some inverse relations (1973) (79)
Generating functions for certain q-orthogonal polynomials (1972) (77)
On abelian fields (1933) (75)
Advanced Problems: 5600-5609 (1968) (75)
Some polynomials related to theta functions (1956) (75)
Primitive roots in a finite field (1952) (74)
A set of polynomials (1940) (70)
The reciprocity theorem for Dedekind sums. (1953) (70)
Note on the Integral of the Product of Several Bernoulli Polynomials (1959) (68)
MAILLET'S DETERMINANT (1955) (66)
Kloosterman sums and finite field extensions (1969) (64)
Expansions of $q$-Bernoulli numbers (1958) (63)
Asymptotic properties of eulerian numbers (1972) (62)
Permutations with prescribed pattern (1973) (62)
Representations by quadratic forms in a finite field (1954) (62)
A theorem of Dickson on irreducible polynomials (1952) (61)
A simple proof of the quintuple product identity (1972) (61)
The inverse of the error function (1963) (58)
The Staudt-Clausen Theorem (1961) (55)
Permutations and sequences with repetitions by number of increases (1966) (52)
The Arithmetic of Polynomials in a Galois Field. (1931) (50)
On some polynomials of Tricomi. (1958) (49)
Permutations in a finite field (1953) (49)
On Jacobi polynomials. (1956) (48)
Eulerian numbers and polynomials of higher order (1960) (48)
The Product of Two Eulerian Polynomials (1963) (46)
The Number of Terms in the Cyclotomic Polynomial F pq (x) (1966) (45)
A note on the Bessel polynomials (1957) (44)
Some theorems on permutation polynomials (1962) (44)
Some Remarks on Ballot-Type Sequences of Positive Integers (1971) (43)
Functions and polynomials ($mod p^n$) (1964) (42)
Single variable bell polynomials (1962) (41)
Note on the Shapiro polynomials (1970) (41)
Representations by skew forms in a finite field (1954) (41)
A note on the Laguerre polynomials. (1960) (41)
A note on certain biorthogonal polynomials. (1968) (41)
Generalized Eulerian numbers combinatorial applications. (1974) (39)
Bernoulli and Euler numbers and orthogonal polynomials (1959) (38)
The singular series for sums of squares of polynomials (1947) (37)
The Arithmetic of Polynomials in a Galois Field (1932) (37)
Irreducibles and the composed product for polynomials over a finite field (1987) (35)
The distribution of irreducible polynomials in several indeterminates (1963) (35)
Polynomials over finite fields with minimal value sets (1961) (35)
Sequences and inversions (1970) (34)
Tangent numbers and operators (1972) (34)
ON A PROBLEM IN ADDITIVE ARITHMETIC (II) (1932) (34)
Representations by Hermitian forms in a finite field (1955) (34)
The number of solutions of a special system of equations in a finite field (1966) (34)
Errata: A Theorem on Permutations in a Finite Field (1960) (33)
Enumeration of pairs of permutations (1976) (33)
Enumeration of sequences by rises and falls: a refinement of the Simon Newcomb problem (1972) (33)
Some theorems on Bernoulli numbers of higher order. (1952) (33)
DISTRIBUTION OF PRIMITIVE ROOTS IN A FINITE FIELD (1953) (33)
A Class of Generating Functions (1977) (32)
The Divided Central Differences of Zero (1963) (32)
An analogue of the von Staudt-Clausen theorem (1937) (32)
Some theorems on irreducible reciprocal polynomials over a finite field. (1967) (32)
Enumeration of up-down sequences (1973) (32)
On Arrays of Numbers (1932) (30)
Some Expansions and Convolution Formulas Related to MacMahon’s Master Theorem (1977) (30)
Some cyclotomic matrices (1959) (30)
SOME REMARKS ON THE BELL NUMBERS (1980) (30)
The Distribution of Irreducible Polynomials in Several Indeterminates II (1965) (29)
Evaluation of some exponential sums over a finite field (1980) (29)
An analogue of the Staudt-Clausen theorem (1940) (29)
Note on some partition formulae (1953) (29)
A problem in partitions related to the Stirling numbers (1964) (29)
Generating functions for powers of certain sequences of numbers (1962) (28)
Gauss sums over finite fields of order $2^n$ (1969) (28)
Rectangular arrays and plane partitions (1967) (28)
Congruences for generalized Bell and Stirling numbers (1955) (28)
NOTE ON IRREGULAR PRIMES (1954) (28)
SOME CONGRUENCES FOR THE BERNOULLI NUMBERS. (1953) (27)
Weighted Quadratic Partitions Over a Finite Field (1953) (27)
A Theorem of Glaisher (1953) (26)
Some generating functions for Laguerre polynomials (1968) (26)
A Binomial Identity Arising from a Sorting Problem (1964) (25)
Some orthogonal polynomials related to elliptic functions (1960) (25)
Note on the numbers of Jordan and Ward (1971) (25)
Scalar Polynomial Functions on the NxN Matrices over a Finite Field. (1975) (25)
Permutations and sequences (1974) (25)
Some polynomials associated with Dedekind sums (1975) (25)
Some Problems Involving Primitive Roots in a Finite Field. (1952) (24)
Some special functions over $GF(q,x)$ (1960) (24)
Permutations, Sequences and Special Functions (1975) (24)
Congruences connected with the power series expansions of the Jacobi elliptic functions (1953) (24)
Sets of primitive roots (1958) (24)
PAIRS OF QUADRATIC EQUATIONS IN A FINITE FIELD. (1954) (23)
A note on permutation functions over a finite field (1962) (23)
A generalization of Maillet’s determinant and a bound for the first factor of the class number (1961) (23)
The product of several Hermite or Laguerre polynomials (1962) (23)
A note on generalized Dedekind sums (1954) (23)
Extended Bernoulli and Eulerian numbers (1964) (23)
Some extensions of the Mehler formula (1970) (23)
A Saalschützian Theorem for Double Series (1963) (22)
Certain special equations in a finite field (1954) (21)
Some properties of Hurwitz series (1949) (21)
Congruence properties of the polynomials of Hermite, Laguerre and Legendre (1953) (21)
Note on irreducibility of the Bernoulli and Euler polynomials (1952) (21)
The number of labeled two-terminal series-parallel networks (1956) (20)
The coefficients of the reciprocal of a series (1941) (20)
The Multiplication Formulas for the Bernoulli and Euler Polynomials (1953) (20)
Multiplication formulas for products of Bernoulli and Euler polynomials (1959) (20)
Some Polynomials of Touchard Connected with the Bernoulli Numbers (1957) (20)
Some determinants of Bernoulli, Euler and related numbers (1959) (20)
Enumeration of rises and falls by position (1973) (20)
The number of binomial coefficients divisible by a fixed power of a prime (1967) (20)
THE EXPANSION OF CERTAIN PRODUCTS (1956) (20)
The coefficients of the reciprocal ofJo(x) (1955) (19)
Finite sums and interpolation formulas over $GF[p^n,x]$ (1948) (19)
Enumeration of symmetric arrays (1966) (19)
Some arithmetic properties of generalized Bernoulli numbers (1959) (19)
Some Properties of the Nörlund Polynomial B (1967) (18)
Congruences for Eulerian numbers (1953) (18)
A theorem of Stickelberger (1953) (18)
The coefficients in an asymptotic expansion (1965) (18)
Some formulas of F. H. Jackson (1969) (17)
Explicit formulas for the Dumont-Foata polynomial (1980) (17)
Invariant theory of systems of equations in a finite field (1953) (17)
Up-down sequences (1972) (17)
Enumeration of Compositions by Rises, Falls and Levels (1977) (17)
Some partition problems related to the Stirling numbers of the second kind (1965) (17)
A q-identity (1963) (16)
Some congruences for the Bell polynomials. (1961) (16)
An Identity of Cayley (1960) (16)
Generating functions for a special class of permutations (1975) (16)
The product of two ultraspherical polynomials (1961) (15)
A PROBLEM IN ADDITIVE ARITHMETIC (15)
The coefficients of certain power series (1955) (15)
Enumeration of permutations by rises, falls, rising maxima and falling maxima (1974) (15)
A note on integral-valued polynomials (1959) (15)
Enumeration of pairs of permutations and sequences (1974) (15)
Some integrals containing products of legendre polynomials (1961) (15)
A sequence of integers related to the Bessel functions (1963) (14)
The relationship of the Hermite to the Laguerre polynomials. (1961) (14)
The generating function for the Jacobi polynomial (1967) (14)
An analogue of the Bernoulli polynomials (1941) (14)
INVARIANTIVE THEORY OF EQUATIONS IN A FINITE FIELD (1953) (14)
DIOPHANTINE APPROXIMATION IN FIELDS OF CHARACTERISTIC p (1952) (14)
Enumeration of matrices with prescribed row and column sums (1973) (14)
A NOTE ON THE MULTIPLICATION FORMULAS FOR THE BERNOULLI AND EULER POLYNOMIALS (1953) (13)
Enumeration of up-down permutations by number of rises (1973) (13)
A note on abelian groups (1953) (13)
A summation theorem for double hypergeometric series (1967) (13)
Generating Functions for Certain Types of Permutations (1975) (13)
Generalized Dedekind sums (1964) (13)
Some generating functions (1963) (13)
Some remarks on a paper by (2005) (13)
Products of Appell polynomials. (1963) (13)
Enumeration of up-down permutations by upper records (1975) (13)
On polynomials in a Galois field (1932) (13)
On a combinatorial identity of Winquist and its generalization (1972) (13)
A Note on Euler Numbers and Polynomials (1954) (12)
On factorable polynomials in several indeterminates (1936) (12)
Note on a Theorem of Glaisher (1953) (12)
A theorem on generalized Dedekind sums (1965) (12)
On the number of distinct values of a polynomial with coefficients in a finite field (1955) (12)
The number of solutions of some equations in a finite field. (1955) (12)
A note on Bernoulli numbers and polynomials of higher order (1952) (12)
A note on exponential sums (1969) (12)
A NOTE ON MULTIPLE EXPONENTIAL SUMS (1965) (12)
Permutations with coefficients in a subfield (1972) (12)
Rational Tabulated Values of Trigonometric Functions (1962) (11)
Some determinants of q-binomial coefficients. (1967) (11)
A Characterization of the n × n Matrices over a Finite Field (1973) (11)
Eulerian numbers and operators (1972) (11)
An integral for the product of two Laguerre polynomials. (1962) (11)
Congruences for the coefficients of the Jacobi elliptic functions (1949) (11)
Note on Nörlund’s polynomial _{}^{()} (1960) (10)
The coefficients of cosh x/cos x (1965) (10)
A note on common index divisors (1952) (10)
Arithmetic properties of elliptic functions (1956) (10)
On Some Special Factorizations of (1-xn)/(1-x) (1966) (10)
Some inversion formulas (1963) (10)
Arithmetic properties of the Bell polynomials (1966) (10)
A Note on the Betti-Mathieu group (1963) (10)
Enumeration of sequences of given specification according to rises, falls and maxima (1974) (10)
Resolvents Of Certain Linear Groups In a Finite Field (1956) (10)
A Note on q-Eulerian Numbers (1978) (10)
Recurrences for the Bernoulli and Euler numbers. (1964) (10)
Enumeration of permutations and sequences with restrictions (1973) (10)
Some Multiple Sums and Binomial Identities (1965) (9)
Some sums involving polynomials in a Galois field (1939) (9)
Note on some continued fractions of the Rogers-Ramanujan type (1965) (9)
Branchings and partitions (1975) (9)
Solvability of certain equations in a finite field (1956) (9)
Note on a Quartic Congruence (1956) (9)
Arithmetic Functions in an Unusual Setting (1966) (9)
Enumeration of permutations by rises and cycle structure. (1973) (9)
Some special equations in a finite field (1953) (9)
On the Product of Two Laguerre Polynomials (1961) (9)
A characterization of the Laguerre polynomials (1962) (9)
Some theorems on Kummer’s congruences (1953) (9)
An Application of MacMahon’s Master Theorem (1974) (9)
A theorem on "ordered" polynomials in a finite field (1962) (9)
Characterization of certain sequences of orthogonal polynomials (1961) (9)
Linear permutation polynomials with coefficients in a subfield (1973) (8)
AN INEQUALITY INVOLVING THE AREA OF TWO TRIANGLES (1971) (8)
Rings of arithmetic functions (1964) (8)
Some Permutation Problems (1977) (8)
A further note on Dedekind sums (1956) (8)
Some theorems on generalized Dedekind-Rademacher sums (1978) (8)
A $q$-analog of a formula of Toscano. (1957) (8)
Some arithmetic properties of theOlivier functions (1954) (8)
Bilinear generating functions for Laguerre and Lauricella polynomials in several variables (1970) (8)
NOTE ON SUMS OF FOUR AND SIX SQUARES (1957) (8)
The inverse of certain formulas involving Bessel functions (1961) (8)
Transformation of arithmetic functions (1973) (8)
On the representation of a polynomial in a Galois field as the sum of an odd number of squares (1933) (7)
Some Functional Equations (1961) (7)
Some theorems on Bernoulli and Euler numbers of higher order (1954) (7)
The Number of Solutions of Certain Equations in a Finite Field. (1952) (7)
Some formulas of Jensen and Gould (1960) (7)
A transformation formula for multiple hypergeometric series (1967) (7)
Independence of arithmetic functions (1952) (7)
Some generalized multiplication formulas for the bernoulli polynomials and related functions (1962) (7)
Multiple sums and generating functions (1965) (7)
The Gegenbauer Addition Theorem (1963) (7)
Congruences for the coefficients of hyperelliptic and related functions (1952) (7)
The number of solutions of some special equations in a finite field. (1954) (7)
Remark on a formula for the Bernoulli numbers (1953) (6)
A CHARACTERIZATION OF PERMUTATION POLYNOMIALS OVER A FINITE FIELD (1978) (6)
A special class of triangular arrays (1976) (6)
Congruences connected with three-line latin rectangles (1953) (6)
A problem in partitions (1963) (6)
Some Combinatorial Identities of Bernstein (1978) (6)
Some orthogonal polynomials related to elliptic functions II. Arithmetic properties (1961) (6)
A note on the enumeration of line chromatic trees (1969) (6)
Solution of Certain Recurrences (1969) (6)
A Note on the Staudt-Clausen Theorem (1957) (6)
Power Sums of Matrices over a Finite Field. II. (1974) (6)
Distribution of matrices in a finite field (1956) (6)
A problem of Dickson’s (1947) (6)
The coefficients of singular elliptic functions (1954) (6)
Dedekind sums and Lambert series (1954) (6)
Some Inequalities for Two Triangles (1972) (6)
Factorization of a special polynomial over a finite field (1970) (6)
Extended Stirling and exponential numbers (1965) (6)
SOME PROBLEMS CONCERNING KUMMER'S CONGRUENCES FOR THE EULER NUMBERS AND POLYNOMIALS (1960) (6)
A Note on Wolstenholme's Theorem (1954) (6)
Representations of arithmetic functions in $GF[p^n,x]$ (1947) (6)
Note on a Paper of Shanks (1952) (6)
Enumeration of certain types of sequences (1971) (6)
Note on a paper of L. Bernstein (1965) (6)
A determinant connected with Fermat’s last theorem (1959) (6)
The number of solutions of certain matric equations over a finite field (1973) (5)
Recurrences for the Rayleigh functions (1967) (5)
A special congruence (1953) (5)
A Quadruple Integral (1967) (5)
Some Formulas for the BERNOULLI and EULER Polynomials (1963) (5)
Note on a Binomial Identity (1975) (5)
Some arithmetic properties of the Legendre polynomials (1957) (5)
Permutations with Prescribed Pattern. II. Applications (1978) (5)
Enumeration of two-line arrays (1973) (5)
A formula connected with lattice points in a circle (1957) (5)
Specialized Möbius Inversion (1978) (5)
Chapter 19 of The Arithmetic of Polynomials (1995) (5)
Sums of squares of polynomials (1937) (5)
Some multiplication formulas (1962) (5)
Quadratic residues and Tchebycheff polynomials (1959) (5)
On A Class of Finite Sums (1930) (5)
Some finite summation formulas of arithmetic character. II (1963) (5)
Criteria for Kummer's congruences (1961) (5)
A test for additive decomposability of irreducibles over a finite field (1989) (5)
Some arithmetic sums connected with the greatest integer function (1961) (5)
Congruence properties of special elliptic functions (1954) (5)
A note on the Eulerian numbers (1963) (5)
Note on a theorem of S. Uchiyama (1959) (5)
Recurrences for the Bernoulli and Euler Numbers. II (1965) (5)
The class number of an imaginary quadratic field (1953) (5)
Generalized Bernoulli and Euler numbers (1941) (5)
Congruence properties of certain polynomial sequences (1960) (5)
Partially ordered sets associated with Fibonacci representations (1973) (5)
Summation of Certain Series (1964) (4)
Some arithmetic properties of a special sequence of polynomials in the Gaussian field (1963) (4)
A problem involving quadratic forms in a finite field (1954) (4)
Note on Alder’s polynomials (1960) (4)
HANKEL DETERMINANTS AND BERNOULLI NUMBERS (1954) (4)
Restricted bipartite partitions. (1966) (4)
A note on permutations in an arbitrary field (1963) (4)
Some new generating functions for the Hermite polynomials (1990) (4)
Some Inequalities for a Triangle (1964) (4)
The First Factor of the Class Number of a Cyclic Field (1954) (4)
The coefficients of the lemniscate function (1962) (4)
The Product of Certain Polynomials Analogous to the Hermite Polynomials (1957) (4)
Arithmetic functions in an unusual setting. II (1967) (4)
A note on the Jacobi theta formula (1962) (4)
Some theorems on the Schur derivative. (1953) (4)
Some generating functions of Weisner (1961) (4)
Some applications of a theorem of Chevalley (1951) (4)
A Note on Stirling Numbers of the First Kind (1964) (4)
A Conjecture Concerning the Euler Numbers (1962) (4)
Some Arithmetic Properties of a Special Sequence of Integers (1976) (4)
Note on Some Convolved Power Sums (1977) (4)
The Number of Coloured Graphs (1963) (4)
Enumeration of certain two-line arrays (1965) (4)
A Property of the Bernoulli Numbers (1959) (4)
The Coefficients of sinh x/sin x (1956) (4)
Kummer's congruences (mod 2r) (1959) (4)
Bernoulli numbers and Bessel polynomials (1959) (4)
Another Saaschützian theorem for double series (1964) (4)
Linear relations among generalized Dedekind sums. (1965) (4)
Weighted quadratic partitions (modpr) (1953) (4)
Multiplication formulas for generalized Bernoulli and Euler polynomials (1960) (4)
Some arithmetic properties of the Bell polynomials (1964) (4)
An arithmetic function (1937) (3)
The generating function for max(n_1,...,n_k) (1962) (3)
A note on the Rogers-Ramanujan identities (1968) (3)
Rectangular arrays of zeros and ones (1972) (3)
A three-term relation for some sums related to Dedekind sums (1975) (3)
The Sign of the Bernoulli and Euler Numbers (1973) (3)
Inequalities for the Area of Two Triangles (1973) (3)
Some Reduction Formulas for Generalized Hypergeometric Functions (1970) (3)
Note on a paper of Dieudonné (1958) (3)
Comment on the Paper “Some Probability Distributions and their Associated Structures” (1964) (3)
Some arithmetic properties of a special sequence of polynomials (1959) (3)
On certain generating functions for the Hermite polynomials (1966) (3)
Enumeration of some two-line arrays by extent (1971) (3)
The distribution of binomial coefficients (modp) (1963) (3)
Congruence properties of the classical orthogonal polynomials (1958) (3)
Note on an Arithmetic Function (1952) (3)
Some applications of Saalschütz's theorem (1970) (3)
Some polynomials related to the ultraspherical polynomials ( (1961) (3)
Note on the class number of real quadratic fields (1953) (3)
Kummer's congruence for the Bernoulli numbers (1960) (3)
A Note on the Rogers‐Ramanujan identities (1958) (3)
Some functions related to Fibonacci and lucas representations (1972) (3)
Remark on a Combinatorial Identity (1974) (3)
A note on the composition of arithmetic functions (1966) (3)
On certain arithmetic functions of several arguments (1937) (3)
A Binomal Identity Related to Ballots and Trees (1973) (3)
The number of solutions of certain types of equations in a finite field. (1955) (3)
A Pair of Identities (1966) (3)
A note on Gauss’ first proof of the quadratic reciprocity theorem (1960) (3)
A Binomial Identity (1967) (3)
SOME EXPANSIONS IN PRODUCTS OF BESSEL FUNCTIONS (1962) (3)
Generalized Turán expressions for certain hypergeometric series (1957) (3)
A characterization of the Bernoulli and Euler polynomials (1980) (3)
Some topics in the arithmetic of polynomials (1942) (3)
A Note on Hermite Polynomials (1955) (3)
Some identities in combinatorial analysis (1971) (3)
The sum of the squares of the coefficients of the cyclotomic polynomial (1967) (3)
Some congruences involving sums of binomial coefficients (1960) (3)
Some continued fraction formulas (1972) (3)
The coefficients of the reciprocal of a Bessel function (1964) (3)
A bilinear generating function for the Hermite polynomials (1961) (3)
The coefficients in an asymptotic expansion and certain related numbers (1968) (3)
A Note on the Generalized Wilson's Theorem (1961) (3)
Some operational equations for symmetric polynomials (1961) (3)
A sorting function (1971) (3)
Linear forms and polynomials in a Galois field (1940) (3)
Some formulas for factorable polynomials in several indeterminates (1937) (2)
A Divisibility Property of the Binomial Coefficients (1961) (2)
Bulygin's method for sums of squares (1973) (2)
On Laguerre and Jacobi polynomials. (1957) (2)
A Double Sum (1968) (2)
A special determinant (1955) (2)
Some functional equations related to binomial coefficient summation (1967) (2)
Some Arithmetic Sums Connected With the Greatest Integer Function. (1960) (2)
On Galois fields of certain types (1930) (2)
Finite summation formulas and congruences for legendre and Jacobi polynomials (1958) (2)
Some generating functions and a binomial identity (1968) (2)
Some unusual congruences for the Bernoulli and Genocchi numbers (1968) (2)
Some integral formulas for the complete elliptic integrals of the first and second kind (1962) (2)
An Addendum to the Paper “A Characterization of the n × n Matrices Over a Finite Field” (1973) (2)
Some q-Analogues of Certain Combinatorial Numbers (1973) (2)
The number of solutions of some congruences modulo a product of primes (1964) (2)
Some Sums Involving Fractional Parts (1975) (2)
Sequences of Absolute Differences (John M. Hammersley) (1970) (2)
A THEOREM OF DICKSON ON NONVANISHING CUBIC FORMS IN A FINITE FIELD (1957) (2)
The generalized hypergeometric differential equation (1968) (2)
Alternating sequences (1977) (2)
Some q‐Polynomials in two Variables (1958) (2)
Sums of primitive roots in a finite field (1952) (2)
Simultaneous representations in quadratic and linear forms over $GF[q,x]$ (1963) (2)
A divisibility property of the Bernoulli polynomials (1952) (2)
KUMMER CONGRUENCES AND THE SCHUR DERIVATIVE. (1953) (2)
Biorthogonal Conditions for a Class of Polynomials (W. A. Chai) (1973) (2)
Transformation of certain bilinear generating functions (1970) (2)
Inversions and generalized Dedekind sums (1974) (2)
Note on the Coefficients of cosh x/cos x (1959) (2)
Note on Schur's expansion of $\sin \pi x$. (1966) (2)
A formula of Bateman (1957) (2)
A System of Difference-Differential Equations (1974) (2)
Composition of secuences satisfying Kummer's congruences (1959) (2)
NOTE ON A PROBLEM OF DICKSON (1963) (2)
A generating function for triangular partitions (1975) (2)
The Irreducibility of the Bernoulli Polynomial B 14 (x) (1965) (2)
The reciprocity theorem for Dedekind-Rademacher sums (1976) (2)
Bateman's expansion for the product of two Bessel functions (1964) (2)
Combinatorial Property of a Special Polynomial Sequence (1977) (2)
Congruences (mod 2r) for the coefficients of the Jacobi elliptic functions (1959) (2)
Enumeration of rectangular arrays by length and coincidences (1974) (2)
Bessel polynomials and Bernoulli numbers (1958) (2)
A special quartic congruence (1956) (2)
Some expansions in theta functions (1962) (2)
The Schur Derivative of a Polynomial (1953) (2)
Note on a Paper of Bagchi and Chatterjee (1952) (2)
The irreducibility of the Bernoulli polynomial (1965) (2)
Note on bilinear generating functions for the Laguerre polynomials. (1961) (2)
Distribution of bordered symmetric, skew and hermitian matrices in a finite field. (1955) (2)
Note on a $q$-identity (1955) (2)
Summation of Some Series of Bessel Functions (1962) (2)
Summation of a special $_{4}F_{3}$. (1963) (2)
A polynomial related to the cyclotomic polynomial (1972) (2)
Some sums connected with quadratic residues (1953) (2)
On the representation of an integer as the sum of twenty-four squares (1955) (2)
Some arithmetic properties of the Chebyshev polynomials (1965) (2)
The factorization of $Q(L(x_1), ..., L(x_k))$ over a finite field where $Q(x_1,...,x_k)$ is of first degree and L(x) is linear (1977) (2)
A note on partitions in (1953) (2)
Problems for Solution: 5092-5100 (1963) (2)
A reciprocity theorem and a three-term relation for generalized Dedekind-Rademacher sums (1980) (2)
Note on the multiplication formulas for the Jacobi elliptic functions. (1955) (2)
An Interpolation Problem (1962) (2)
A note on Gauss’ sum (1956) (2)
Some Congruence Properties of the Legendre Polynomials (1961) (2)
A note on Bernoulli and Euler numbers of order (1953) (2)
Some Finite Analogues of the Poisson Summation Formula (1961) (2)
Some sums analogous to Dedekind sums (1953) (2)
Problems for Solution: 4718-4722 (1957) (2)
A recurrence formula for (2) (1961) (1)
Note on a paper of GÖTZE (1967) (1)
Note on the Cyclotomic Polynomial (1954) (1)
On a theorem of higher reciprocity (1933) (1)
Some formulas of E. Feldheim (1963) (1)
Covering theorems for finite nonabelian simple groups. III. - Solutions of the equation $\alpha x^2 + \beta t^2 + \gamma t^{-2} = a$ in a finite field (1976) (1)
Some hypergeometric congruences (1953) (1)
A multiple sum (1962) (1)
Sums of arithmetic functions (1969) (1)
Bessel polynomials and Bernoulli numbers (1958) (1)
Some integral equations satisfied by theta functions. (1959) (1)
Some difference equations (1966) (1)
Some orthogonal functions in several variables related to theta functions (1958) (1)
A Note on the Greatest Integer Function (1974) (1)
The highest power of a prime dividing certain quotients (1967) (1)
A Theorem on Differential Operators (1976) (1)
Functions and correspondences in a finite field (1977) (1)
Problems for Solution: E1451-E1455 (1961) (1)
Some Arithmetic Properties of the Lemniscate Coefficients (1960) (1)
Note on Certain Triangular Arrays (1970) (1)
Congruence properties of certain linear homogeneous difference equations (1962) (1)
A System of Second Order Differential Equations (1977) (1)
A Unique Solution (D. J. Newman) (1971) (1)
Congruence properties of the Weierstrass al-functions (1960) (1)
Remarks on MacMahons identity for sums of cubes of binomial coefficients (2007) (1)
On a function connected with a cubic field (1931) (1)
Mathematical Pearls: A Recurrence Formula for ζ(2n) (1961) (1)
A note on Saalschützian double series (1970) (1)
A theorem on higher congruences (1935) (1)
Three Multiple Summations (1976) (1)
Some Product-Sum Identities (1978) (1)
Advanced Problems: 6006-6011 (1975) (1)
Some Theorems on Polynomials Over a Finite Field (1977) (1)
Problems for Solution: 4773-4777 (1958) (1)
Class number formulas for quadratic forms over $GF[q,x]$ (1956) (1)
A Theorem of Schemmel (1966) (1)
An integral formula for the Jacobi polynomial. (1962) (1)
Classes of Pairs of Commuting Matrices over a Finite Field (1963) (1)
Advanced Problems: 5324-5379 (1966) (1)
A short proof of Jacobi’s four square theorem (1966) (1)
Some Combinatorial Identities of Sarmanov, Sevast'yanov, and Tarakanov (1977) (1)
Problems for Solution: 4941-4946 (1961) (1)
On some differential and integro-differential equations associated with Jaocobi's differential equation. (1976) (1)
A Sum Connected with Quadratic Residues (1956) (1)
On certain equations in relative-cyclic fields (1936) (1)
The reciprocal of certain types of Hurwitz series (1942) (1)
The bilinear generating funktion for hermite polynomials in several variables (1957) (1)
A congruence for the second factor of the class number of a cyclotomic field (Corrigendum) (1968) (1)
Divisor functions of polynomials in a Galois field (1947) (1)
A Correction for "Classes of Pairs of Commuting Matrices Over a Finite Field" (1964) (1)
An Extension of the Fermat Theorem (1963) (1)
APPLICATIONS OF SOME BASIC IDENTITIES (1953) (1)
A Note on Sums of Powers of Integers (1962) (1)
A note on nonsingular forms in a finite field (1956) (1)
Advanced Problems: 5270-5279 (1965) (1)
Correspondences in a finite field, I (1975) (1)
The Sum of the Angles in an n-Dimensional Simplex (1961) (1)
Congruences for the solutions of certain difference equations of the second order (1954) (1)
A Note on Circumscriptible Cyclic Quadrilaterals (1965) (1)
On the complete elliptic integral of the third kind. (1960) (1)
Corrigendum to the paper. Generalized Eulerian numbers: combinatorial applications (this Journal vol. 265 (1974), 110—137) (1976) (1)
Characterizations of the krawtchouk polynomials (1961) (1)
On two combinatorial identities (1982) (1)
Congruences for the ménage polynomials (1952) (1)
Up-down permutations of higher order. (1980) (1)
The sum of the first $n$ terms of an $_{5}F_{4}$. (1964) (1)
Some Operational Formulas (1970) (1)
A congruence satisfied by the theta-constant ₃ (1959) (1)
Problems for Solution: 4617,4628-4632 (1955) (1)
Reduction formulas for certain multiple exponential sums (1970) (0)
Some theorems on polynomials (1957) (0)
A Positive Integral (1971) (0)
Problems for Solution: 4528-4532 (1953) (0)
Advanced Problems: 5380-5389 (1966) (0)
An Infinite Summation (S. Saran) (1972) (0)
NOTE ON SOME PARTITION IDENTITIES (1953) (0)
Advanced Problems: 5826-5831 (1971) (0)
Problems Dedicated to Emory P. Starke: S26 (1980) (0)
Problems for Solution: 5013-5018 (1962) (0)
Advanced Problems: 5646,5671-5676 (1969) (0)
A Formula for the Product of Two Hermite Polynomials (1957) (0)
Congruences for the Number of n-gons Formed by n Lines (1960) (0)
An Infinite Set of Simultaneous Equations (1969) (0)
Enumeration of doubly up-down permutations (1977) (0)
Note a formula of Witt (1966) (0)
A note on Dougall's theorem. (1964) (0)
Simultaneous inversions (1976) (0)
Problems for Solutions: 5111-5120 (1963) (0)
SOME CONGRUENCES OF VANDIVER. (1953) (0)
Restricted product of the characteristic polynomials of matrices over a finite field (1967) (0)
Shorter Notes: A Short Proof of Jacobi's Four Square Theorem (1966) (0)
A note onKummer's congruences (1957) (0)
Enumeration of sequences by length and spread (1967) (0)
Elementary Problems: E1995-E2005 (1967) (0)
A Theorem on Lacunary Polynomials in a Finite Field (1976) (0)
A note on representations of quadratic forms (1956) (0)
Some Limits Involving Binomial Coefficients (1966) (0)
Errata: The Number of Solutions of Certain Equations in a Finite Field (1952) (0)
Advanced Problems: 5736,5746-5752 (1970) (0)
Some Formulas of Oltramare (1954) (0)
On Polynomials in a Galois Field: Some Formulae Involving Divisor Functions (1935) (0)
A functional-difference equation (1964) (0)
A Hyperbolic Series Identity (Chih-Bong Ling) (1980) (0)
A theorem on multiple power series with integral coefficients (1968) (0)
Some formulas related to Gauss's sum (1968) (0)
Criteria for Certain Higher Congruences (1937) (0)
A Remark on Cubics (1966) (0)
A Set of Nonlinear Equations (1972) (0)
Problems for Solution: 4758-4762 (1957) (0)
The coefficients in the expansion of certain products (1962) (0)
Two Laurent Expansions (1971) (0)
The product of q-Bessel functions (1962) (0)
Explicit Evaluation of Certain Polynomials (1972) (0)
SOME IDENTITIES OVER A FINITE FIELD (1962) (0)
Errata: “Bernoulli and Euler numbers and orthogonal polynomials,” vol. 26 (1959), pp. 1–15 (1959) (0)
Expansion of a special operator (1978) (0)
Note on a conjecture of André Weil (1953) (0)
Problems for Solution: 4693-4697 (1956) (0)
A Network Inequality (J. C. Turner and V. Conway) (1969) (0)
A problem in factorization of polynomials (1955) (0)
Problems for Solution: 4639,4643-4647 (1955) (0)
A note on power series with integral coefficients. (1964) (0)
The Coefficients of the k-th Power of a Power Series With Integral Coefficients (1964) (0)
A theorem of Ljunggren and Jacobsthal on Bernoulli numbers (1954) (0)
Abstracts from papers (1995) (0)
Note on diophantine automorphisms (1932) (0)
Note on a Formula of Hermite (1959) (0)
Advanced Problems: 5200-5208 (1964) (0)
Some integral equations satisfied by the complete elliptic integrals of the first and second kind. (1961) (0)
A Note on the Hardy-Hille and Mehler formulas (1965) (0)
A note on some special polynomials (1958) (0)
Errata: “Note on the class number of quadratic fields,” vol. 22 (1955), pp. 589–594 (1960) (0)
Criteria for Generalized Kummer's Congruences. (1961) (0)
Hurwitz series: Eisenstein criterion (1949) (0)
A Set of Linear Equations (Peter H. Astor) (1971) (0)
On certain higher congruences (1935) (0)
A Combinatorial Problem (Joseph Arkin) (1967) (0)
Advanced Problems: 5209-5217 (1964) (0)
Arithmetic properties of certain polynomial sequences (1960) (0)
The number of representations of a polynomial in certain special quadratic forms (1948) (0)
A special symmetric equation in a finite field (1955) (0)
A generating function for the product of two ultraspherical polynomials. (1959) (0)
A Note on Orthogonal Matrices (1953) (0)
Bracket Function Congruences for Binomial Coefficients (1964) (0)
A Note on Selfadjoint Operators (1966) (0)
Elementary Problems: 2349,E2350-E2354 (1972) (0)
The reciprocal of certain series (1942) (0)
Some congruences involving binomial coefficients (1966) (0)
Problems for Solution: 4933, 4953-4958 (1961) (0)
Problems for Solution: 5101-5110 (1963) (0)
An extension of Bauer's congruence (1955) (0)
Weighted quadratic partitions over $GF[q,x]$ (1956) (0)
Cauchy products of divisor functions in $GF[p^n,x]$ (1947) (0)
TOPICS IN ANALYTIC NUMBER THEORY (1975) (0)
Advanced Problems: 5397,5410- 5419 (1966) (0)
Problems for Solution: 4513-4517 (1952) (0)
SOME PARTITION FORMULAS (1954) (0)
Elementary Problems: E2265-E2270 (1970) (0)
Problems for Solution: 4788-4792 (1958) (0)
Polynomial characteristic functions for $GF(p)$ and irregular primes (1978) (0)
NOTE ON SOME FORMULAS OF RODEJA F. (1953) (0)
Correction to the paper "Binomial coefficients in an algebraic number field" (1966) (0)
A Pair of Theta Function Identities (1973) (0)
Advanced Problems: 5143,5191-5199 (1964) (0)
Problems for Solution: 4598-4602 (1954) (0)
A Note on Exponents (MOD 2 r ) (1964) (0)
THE PRODUCT OF BASIC BESSEL FUNCTIONS (1960) (0)
THE NOVEMBER MEETING IN UNIVERSITY, ALABAMA The five hundred and seventh meeting of the American Mathe- (2007) (0)
Characterization of certain $q$-identities. (1964) (0)
Problems for Solution: E1621-E1630 (1963) (0)
A Note on Sums of Three Squares in Gf[q, x] (1975) (0)
Problems for Solution: 4783-4787 (1958) (0)
The euler-fermat property in a polynomial domain (1963) (0)
Some Sums Containing Bernoulli Functions (1953) (0)
Weighted two-line arrays (1965) (0)
Problems for Solution: E1597,E1611-E1620 (1963) (0)
Some class number relations (1955) (0)
Remark on a formula of P.H. Jackson (1970) (0)
A Recursion Relation (E. L. Pugh) (1966) (0)
Advanced Problems: 5575,5610-5619 (1968) (0)
A TRANSFORMATION FORMULA FOR AN 4F3 (1969) (0)
An Inequality for the Perimeter of the Orthic Triangle (1966) (0)
Solution of Certain Recurrences. II (1978) (0)
Some Multiple Power Series with Zero-One Coefficients (1979) (0)
Problems for Solution: 4683-4687 (1956) (0)
Problems for Solution: 4743-4747 (1957) (0)
Binomial coefficients in an algebraic number field (1962) (0)
Problems for Solution: 5157,5181-5190 (1964) (0)
Advanced Problems: 5218-5226 (1964) (0)
A note on some polynomial identities (1980) (0)
A theorem on sets of polynomials over a finite field (1969) (0)
An addition theorem for the confluent hypergeometric series (1964) (0)
A Stock Market Investment Inequality (M. J. Lempel) (1971) (0)
A note on power residues (1955) (0)
Problems for Solution: E1506-E1510 (1962) (0)
EULER'S NUMBERS AND THE DIOPHANTINE EQUATION xl+ yl = czt (1973) (0)
Problems for Solution: 3951, 4810-4815 (1958) (0)
Elementary Problems: E2045-E2054 (1968) (0)
Note on the class number of quadratic fields (1955) (0)
A reciprocity formula for weighted quadratic partitions (1953) (0)
Sums of primitive roots of the first and second kind in a finite field (1954) (0)
New diophantine automorphisms (1932) (0)
Problems for Solution: 4768-4772 (1958) (0)
CORRIGENDUM TO: ENUMERATION OF TWO-LINE ARRAYS (1973) (0)
NOTE ON LEBESGUE'S CONSTANTS (1961) (0)
Elementary Problems: E2293-E2294,E2343-E2348 (1972) (0)
A note on finite fields (1962) (0)
Advanced Problems: 6183,6210-6215 (1978) (0)
Note on a Formula of Grosswald (1953) (0)
A note on quadrics over a finite field (1966) (0)
A Positive Integral (Richard Askey) (1970) (0)
Enumeration of matrices of given rank with submatrices of given rank (1977) (0)

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