Louis J. Mordell
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American-born British number theorist
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Louis J. Mordellmathematics Degrees
Mathematics
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Number Theory
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Measure Theory
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Mathematics
Why Is Louis J. Mordell Influential?
(Suggest an Edit or Addition)According to Wikipedia, Louis Joel Mordell was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction.
Louis J. Mordell's Published Works
Number of citations in a given year to any of this author's works
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
- Diophantine equations (1969) (611)
- On the Evaluation of Some Multiple Series (1958) (98)
- The diophantine equationz2=ax4+2bx2y2+cy4 (1967) (85)
- On lattice points in n-dimensional star bodies I. Existence theorems (1946) (82)
- Lattice Points in a Tetrahedron and Generalized Dedekind Sums (1951) (81)
- THE RIEMANN HYPOTHESIS AND HILBERT'S TENTH PROBLEM (1966) (71)
- ON A SUM ANALOGOUS TO A GAUSS'S SUM (1932) (61)
- The Integer Solutions of the Equation y2 = axn+bxn−1+…+k (1926) (56)
- Review: J. W. S. Cassels, An introduction to the geometry of numbers (1961) (56)
- A NEW WARING'S PROBLEM WITH SQUARES OF LINEAR FORMS (46)
- Observation on the Minimum of a Positive Quadratic Form in Eight Variables (1944) (43)
- The Congruence (p - 1/2)! ≡± 1 (mod p) (1961) (42)
- On the Integer Solutions of the Equation x2+y2+z2+2xyz = n (1953) (42)
- On the integer solutions of $y(y+1)=x(x+1)(x+2)$. (1963) (41)
- Elementary methods in analytic number theory (1967) (38)
- The definite integral $$\int\limits_{ - \infty }^\infty {\tfrac{{e^{ax^2 + bx} }}{{e^{ax} + d}}da} $$ and the analytic theory of numbersand the analytic theory of numbers (1933) (37)
- Elementary Methods in the Analytic Theory of Numbers (1966) (34)
- THE RECIPROCITY FORMULA FOR DEDEKIND SUMS. (1951) (33)
- Poisson's Summation Formula and the Riemann Zeta Function (1929) (32)
- The Present State of Some Problems in the Theory of Numbers (31)
- The Representation of a Definite Quadratic Form as a Sum of Two Others (1937) (28)
- On the representation of a binary quadratic form as a sum of squares of linear forms (1932) (28)
- On the linear independence of algebraic numbers. (1953) (28)
- On a Pellian equation conjecture (1960) (26)
- Poisson's Summation Formula in several Variables and some Applications to the Theory of Numbers (1929) (25)
- On the Integer Solutions of the Equation ey2 = ax3+bx2+cx+d (24)
- Integral Formulae of Arithmetical Character (1958) (24)
- The Approximate Functional Formula for the Theta Function (1926) (23)
- Note on Certain Modular Relations Considered by Messrs. Ramanujan, Darling, and Rogers (20)
- On the number of solutions in incomplete residue sets of quadratic congruences (1957) (19)
- On the inequality $$\sum\limits_{r = 1} {x_r /(x_{r + 1} + x_{r + 2} ) \geqslant n/2} $$ and some othersand some others (1958) (19)
- The diophantine equation Ax4 + By4 + Cz4 = 0 (1970) (19)
- The Product of Three Homogeneous Linear Ternary Forms (1942) (18)
- A Remark on Indeterminate Equations in Several Variables (1937) (18)
- On some arithmetical results in the geometry of numbers (1935) (17)
- On the magnitude of the integer solutions of the equation ax2 + by2 + cz2 = 0 (1969) (17)
- The Diophantine Equation y2−k=x3 (17)
- Review: Z. I. Borevich and I. R. Shafarevich, Number theory (1965) (16)
- On a Pellian Equation Conjecture (II) (1961) (16)
- On Power Series with the Circle of Convergence as a Line of Essential Singularities (1927) (16)
- On the Conjecture for the Rational Points on a Cubic Surface (1965) (15)
- THE DIOPHANTINE EQUATION x4+my4 =z2 (1967) (15)
- On the Kusmin-Landau inequality for exponential sums (1958) (14)
- Irrational power series (1961) (13)
- On Numbers Represented by Binary Cubic Forms (1945) (13)
- Note on an Arithmetical Problem on Linear Forms (1937) (12)
- The number of solutions of some congruences in two variables (1933) (12)
- The representation of integers by three positive squares. (1960) (12)
- On the Geometry of Numbers in Some Non-Convex Regions (1945) (11)
- On the Riemann Hypothesis and Imaginary Quadratic Fields with a Given Class Number (1934) (11)
- The sign of the Gaussian sum (1962) (11)
- Incomplete exponential sums and incomplete residue systems for congruences (1964) (11)
- The Diophantine equationy2=ax3+bx2+cx+d (1964) (11)
- On the equation ax2+by2−cz2=0 (1951) (10)
- On the exponential sum (1972) (10)
- Lattice Points in the Region |Ax4+By4| ⩽ 1 (1941) (10)
- Tschebotareff's Theorem on the Product of Non‐Homogeneous Linear Forms (II) (1960) (9)
- Guide to Tables in the Theory of Numbers (1943) (9)
- Some Applications of Fourier series in the Analytic Theory of Numbers (1928) (9)
- The Diophantine Equation y2 = Dx4+1 (1964) (9)
- Hardy's “a Mathematician's Apology” (1970) (9)
- An identity in combinatorial analysis (1962) (9)
- Reminiscences of an Octogenarian Mathematician (1971) (9)
- On the Minimum of a Ternary Cubic Form (1944) (8)
- A SELECTION OF PROBLEMS IN THE THEORY OF NUMBERS (1965) (8)
- The Diophantine equation $x^4 + y^4 = 1$ in algebraic number fields (1968) (8)
- Foundations of the Theory of Algebraic Numbers (1933) (7)
- A chapter in the theory of numbers (1947) (7)
- Systems of Congruences (1973) (7)
- On the Least Residue and Non-Residue of a Polynomial (1963) (7)
- The Diophantine Equation y2=ax3+bx2+cx+d, Or Fifty Years After (1963) (7)
- Note on the Inequality ∑r=1nxr/(xr+1+xr+2) ≥ ½n (1962) (7)
- Three Lectures On Fermat's Last Theorem (1922) (7)
- Foundations of the Theory of Algebraic Numbers (1932) (7)
- On Geometric Problems of Erdös and Oppenheim (1962) (6)
- AN APPLICATION OF QUATERNIONS TO THE REPRESENTATION OF A BINARY QUADRATIC FORM AS A SUM OF FOUR LINEAR SQUARES (1937) (6)
- The Infinity of Rational Solutions of y2 = x3 +k (1966) (6)
- Integer Quotients of Products of Factorials (1959) (5)
- Note on the product of n inhomogeneous linear forms (1972) (5)
- Minkowski's Theorem on the Product of Two Linear Forms (5)
- The congruenceax3+by3+c≡0 (modxy), and integer solutions of cubic equations in three variables (1952) (5)
- THE ZETA FUNCTIONS ARISING FROM QUADRATIC FORMS, AND THEIR FUNCTIONAL EQUATIONS (5)
- Gesammelte Abhandlungen. III. Analysis. Grundlagen der Mathematik. Physik. Verschiedenes nebst einer Lebensgeschichte (1936) (5)
- On the Number of Solutions in Positive Integers of the Equation yz + zx + xy = n (5)
- The diophantine equation 2n=x2+7 (1962) (5)
- Review: Serge Lang, Diophantine geometry (1964) (5)
- The Minimum Value of a Definite Integral (1968) (5)
- Solvability of the Equation ax2+By2 = p (1966) (5)
- On Hecke's Modular Functions, Zeta Functions, and some Other Analytic Functions in the Theory of Numbers (1931) (5)
- On Some Diophantine Equations y2 = x3 + k with no Rational Solutions (II) (1969) (4)
- On a cyclotomic resolvent (1962) (4)
- Irrational power series II (1965) (4)
- The arithmetically reduced indefinite quadratic form in n-variables (1931) (4)
- Irrational power series. III (1965) (4)
- The Minimum of a Definite Ternary Quadratic Form (1948) (4)
- On lattice points in the domain |xy | ≤1, | x + y | ≤√5, and applications to asymptotic formulae in lattice point theory (II) (1944) (4)
- On Lehmer's Congruence Associated with Cubes of Kloosterman's Sums (1961) (4)
- On some exponential sums related to Kloosterman sums (1972) (4)
- Integer solutions of simultaneous quadratic equations (1959) (4)
- Some aspects of Davenport's work (1971) (4)
- Two papers on number theory (1972) (4)
- Some quartic diophantine equations of genus 3 (1966) (4)
- Expansion of a function in a series of Bernoulli polynomials, and some other polynomials (1966) (4)
- On an Infinity of Integer Solutions of ax3+ay3+bz3=bc3 (1955) (4)
- An arithmetical theorem on linear forms (1936) (3)
- On Sums of Three Cubes (1942) (3)
- Thoughts on Number Theory (1946) (3)
- On a Discriminant Inequality (1960) (3)
- On the Reciprocity Formula for the Gauss's Sums in the Quadratic Field (3)
- The representation of numbers by some quaternary quadratic forms (1966) (3)
- A NEW TYPE OF EXPONENTIAL SERIES (1972) (3)
- The minimum value of a definite integral II (1969) (3)
- Note on a Harmonic Double Series (1960) (3)
- Kronecker's Fundamental Limit Formula in the Theory of Numbers and Elliptic Functions, and Similar Theorems (1929) (3)
- On Ingham's trigonometric inequality (1957) (3)
- The Putnam Competition (1963) (3)
- A Summability Convergence Theorem (1928) (3)
- On some sextic diophantine equations of genus 2 (1969) (3)
- The Minimum of a Singular Ternary Quadratic Form (1970) (3)
- The Product of Homogeneous Linear Forms (1941) (2)
- Note on Cubic Diophantine Equations z2 = f(x, y) with an Infinity of Integral Solutions (1942) (2)
- Some Diophantine inequalities (1955) (2)
- On a cubic congruence in three variables (1962) (2)
- On a cubic congruence in three variables. II (1963) (2)
- The Minimum of a Binary Cubic Form (II) (1943) (2)
- Binary Cubic Forms Expressed as a Sum of Cubes of Seven Linear Forms (1967) (2)
- A finite evaluation of a special exponential sum (1972) (2)
- On the Convergence of a certain Multiple Series (1929) (2)
- Review: A. E. Gelfond and U. V. Linnik, Elementary methods in analytic number theory (1964) (2)
- The minima of some non-homogeneous functions of two variables (1952) (2)
- Note on the nonvanishing of L(1) (1961) (2)
- The minimum of a non-homogeneous binary cubic form (1952) (2)
- On binary quadratic forms expressable as a sum of three linear squares with integer coefficients. (1932) (2)
- The Representation of a Gaussian Integer as a Sum of Two Squares (1967) (2)
- Note on Sawyer's Paper “The Product of Two Non‐Homogeneous Linear Forms” (1953) (2)
- Harold Davenport (1907-1969) (1971) (2)
- On the Product of Two Non-Homogeneous Linear Forms (1941) (2)
- The minimum of an inhomogeneous quadratic polynomial inn variables (1955) (2)
- On the Four Integer Cubes Problem (1936) (2)
- Note on the diophantine equation $ax^2 + by^2 + cz^2 + dt^2 = 0$ (1932) (2)
- The Magnitude of the Derivative of a Function (1928) (2)
- Lattice Octahedra (1960) (2)
- Note on the Linear Symmetric Congruence in n Variables (1953) (2)
- On Rational Functions Representing All Residues Mod P (1972) (2)
- Integer Solutions of the Equation x2+y2+z2+2xyz = n (1957) (2)
- A Congruence Problem of E. G. Straus (1963) (2)
- Some Results in the Geometry of Numbers for Non‐Convex Regions (1941) (2)
- On Lerch's class number formulae for binary quadratic forms (1963) (2)
- The Sign of the Bernoulli Numbers (1973) (2)
- Lattice Points in the Region |x3+y|⩽1 (1944) (2)
- Some exponential sums in several variables (1969) (1)
- On Some Ternary Quartic Diophantine Equations. (1966) (1)
- A chapter in the theory of numbers : an inaugural lecture (1947) (1)
- The Series Σan /(1−xe2n πiα ) (1963) (1)
- On Trigonometric Series Involving Algebraic Numbers (1)
- Note on cubic equations in three variables with an infinity of integer solutions (1949) (1)
- A Theorem of Khintchine on Linear Diophantine Approximation (1937) (1)
- 1570. Note on an entry in Lewis Carroll’s diary (1942) (1)
- The condition for integer solutions of ax2 + by2 + cz2 + dt2 = 0. (1931) (1)
- On sums of four cubes of polynomials (1972) (1)
- Further contribution to the geometry of numbers for non-convex regions (1946) (1)
- A theorem of Minkowski on the product of two linear forms (1953) (1)
- Rational Points on Cubic Curves and Surfaces (1944) (1)
- Expansion of a Function in Terms of Bernouilli Polynomials (1966) (1)
- Segre's Indeterminate Non‐Homogeneous Cubic Equation in Three Variables (1943) (1)
- The lattice points in a parallelogram (1930) (1)
- On the number of representations of an integer as the sum of three r-free integers (1947) (1)
- HOMOGENEOUS LINEAR FORMS IN ALGEBRAIC FIELDS (1937) (1)
- Dirichlet's Integrals (1944) (1)
- On cubic equations ²=(,) with an infinity of integer solutions (1952) (1)
- On Ryley's Solution of x3+y3+z3 = n (1942) (1)
- Cubic Polynomials with the Same Residues mod p (1970) (1)
- The Diophantine Equations y2 = x4 ± 1 in Quadratic Fields (1969) (1)
- On the Representation of a Binary Cubic Form as a Sum of Cubes (1936) (1)
- On the representation of positive integers as sums of three cubes of positive rational numbers (1971) (1)
- An application of Minkowski's theorem in the geometry of numbers (1972) (1)
- Note on Kapteyn's and Bateman's Integrals Involving Bessel Functions (1930) (1)
- Note on simultaneous quadratic congruences (1957) (1)
- On the congruence $ax^3+by^3+cz^3+dxyz \equiv n(\mod p)$ (1964) (1)
- The Product of Two Non‐Homogeneous Linear Forms (III) (1943) (1)
- Über die Klassenzahl Abelscher Zahlkörper. By H. Hasse Pp. ix, 190. $6.48. 1952. (Akademie Verlag, Berlin) (1953) (1)
- Review: M. Deuring, Die Klassenkörper der komplexen Multiplikation (1960) (1)
- 3) Diophantine Approximation (1950) (0)
- Equations ax3+bx2y + cxy2+dy3 = e with no Rational Solutions (1968) (0)
- An introductory account of the arithmetical theory of algebraic numbers and its recent developments (1923) (0)
- 2609. Transport problem (1956) (0)
- Elementary Problems: E1995-E2005 (1967) (0)
- Mathematicians and their Work (1921) (0)
- Review: E. Artin, Theory of algebraic numbers (1962) (0)
- On Salié's sum (1973) (0)
- The diophantine equation $dy^2 = ax^4 + bx^2 + c$ (1969) (0)
- On An Arithmetical Functional Equation in the Theory of the Elliptic Algebraic Function Fields (1936) (0)
- Newton's Work in Pure Mathematics (1927) (0)
- The Convergence of Series Summable (C, r) (1928) (0)
- On Numbers which can be Expressed as a Sum of Powers (1969) (0)
- On the Minimum of a Binary Cubic Form (1941) (0)
- British Association for the Advancement of Science. Mathematical Tables. VIII. Number-Divisor Tables (1941) (0)
- Problems for Solution: 4558-4562 (1953) (0)
- A Rational Parametric Solution of z2−k = ax3+bx2y+cxy2+dy3 (1943) (0)
- Linear substitutions arising from series of eisenstein’s type (1929) (0)
- On a Cubic Exponential Sum in Two Variables (1963) (0)
- On a Cubic Exponential Sum in Three Variables (1963) (0)
- Fermat's Last Theorem: Proofs by Elementary Algebra (1921) (0)
- David Hilbert. Gesammelte Abhandlungen. I. Zahlentheorie (1932) (0)
- David Hilbert. Gesammelte Abhandlungen. II. Algebra, Invarianten-theorie, Geometrie (1934) (0)
- On An Arithmetical Formula (1929) (0)
- Minkowski's Theorem on Homogeneous Linear Forms (1933) (0)
- Mathematical Tables. V. Factor Table Giving the Complete Decomposition of All Numbers Less than 100,000 (1936) (0)
- On a theorem of L. J. Mordell (1961) (0)
- Average and Probability: 181-182 (1906) (0)
- Book Review: An introduction to the geometry of numbers (1961) (0)
- On the sign of a multiple integral (1963) (0)
- Two statements concerning the article on G. H. Hardy (1949) (0)
- On the Product of Two Linear Homogeneous Forms (1938) (0)
- Rational functions representing all residues . II (1972) (0)
- On a distance-function inequality and A. Brauer’s inequality for Cassini curves (1958) (0)
- Problems for Solution: 4683-4687 (1956) (0)
- Fermat’s Last Theorem—Proofs by Elementary Algebra. By M. Cashmore. 3rd Edition. Pp. 31. 4s. net. 1921. (Bell & Sons.) (1921) (0)
- Note on some linear Diophantine Inequalities (1930) (0)
- On intervals containing an affinely equivalent set of $n$ integers mod $k$ (1954) (0)
- Calculus: 240-241 (1907) (0)
- Addendum to: “Some quartic diophantine equations of genus 3” (1967) (0)
- Rational Functions Representing All Residues Mod p. II (1972) (0)
- A Linear Form Result in the Geometry of Numbers (1972) (0)
- On a Circular Region Enclosing a Root of An Algebraic Equation (1929) (0)
- The Integer Solutions of the Equation ax2+by2+c = 0 in Quadratic Fields (1969) (0)
- An irreducible non-convex region (1953) (0)
- Mathematical Tables. III. Minimum Decompositions into Fifth Powers (1934) (0)
- On the region defined by | xy | ≤ 1, x2 + y2 ≤ t (1953) (0)
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