Andrzej Schinzel | Academic Influence

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Andrzej Schinzel

Mathematics

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Measure Theory

#1248

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#1583

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Mathematics

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According to Wikipedia, Andrzej Bobola Maria Schinzel was a Polish mathematician studying mainly number theory. Education Schinzel received an MSc in 1958 at Warsaw University, Ph.D. in 1960 from Institute of Mathematics of the Polish Academy of Sciences where he studied under Wacław Sierpiński, with a habilitation in 1962. He was a member of the Polish Academy of Sciences.

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Andrzej Schinzel'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

Perturbation theory of Kepler motion based on spinor regularization. (1965) (656)
Polynomials with Special Regard to Reducibility (2000) (272)
Selected topics on polynomials (1982) (206)
On the product of the conjugates outside the unit circle of an algebraic number (1973) (146)
A Combinatorial Problem Connected with Differential Equations (1965) (145)
Polynomials with Special Regard to Reducibility: Index of terms (2000) (122)
Primitive divisors of the expression An - Bn in algebraic number fields. (1968) (115)
On the equation $y^m = P(x)$ (1976) (97)
EQUATIONS OF THE FORM f(x)=g(y) (1961) (89)
On Primitive Prime Factors of an-bn (1962) (72)
A refinement of two theorems of Kronecker. (1965) (71)
On two theorems of Gelfond and some of their applications (1967) (62)
Abelian binomials, power residues and exponential congruences (1977) (59)
On some problems of the arithmetical theory of continued fractions (1961) (54)
Reducibility of polynomials and covering systems of congruences (1967) (50)
Self-Inversive Polynomials with All Zeros on the Unit Circle (2005) (46)
Polynomials with Special Regard to Reducibility: Preface (2000) (41)
Arithmetical Properties of Polynomials (2013) (38)
On Pythagorean triangles (1998) (37)
On Sylow 2-subgroups of K2OF for quadratic number fields F. (1982) (36)
The intrinsic divisors of Lehmer numbers in the case of negative discriminant (1962) (35)
Representations of multivariate polynomials by sums of univariate polynomials in linear forms (2008) (33)
Polynomials of certain special types (1964) (30)
Reducibility of lacunary polynomials, III (1969) (28)
Small solutions of quadratic congruences and small fractional parts of quadratic forms (1980) (28)
On Siegel's zero (1975) (27)
On testing the divisibility of lacunary polynomials by cyclotomic polynomials (2003) (26)
Selmer's Conjecture and Families of Elliptic Curves (1982) (26)
Reducibility of polynomials in several variables. II. (1985) (26)
Errata to the paper "On the reducibility of polynomials and in particular of trinomials" (1965) (24)
On the functions φ(n) and σ(n) (1964) (23)
On primitive prime factors of Lehmer numbers I (1963) (23)
On the number of terms of a power of a polynomial. (1987) (22)
On reducible trinomials, III (2002) (22)
Addition of sequences in general fields (1976) (22)
Number Theory and Polynomials: Irreducibility and greatest common divisor algorithms for sparse polynomials (2008) (21)
A Tribute to Paul Erdős: Special Lucas sequences, including the Fibonacci sequence, modulo a prime (1990) (21)
Polynomials with Special Regard to Reducibility: Polynomials over a number field (2000) (20)
On difference polynomials and hereditarily irreducible polynomials (1980) (19)
Reducibility of quadrinomials (1972) (19)
Reducibility of lacunary polynomials II (1970) (19)
On linear dependence of roots (1975) (18)
A Property of Polynomials with an Applicationto Siegel’s Lemma (2002) (17)
An inequality for determinants with real entries (1978) (17)
On $n$ numbers on a circle (1988) (16)
Corrigendum to “Representatons of multivariate polynomials by sums of univariate polynomials in linear forms” (Colloq. Math. 112 (2008), 201–233) (2011) (16)
A refinement of a theorem of Gerst on power residues (1970) (15)
The least admissible value of the parameter in Hilbert's Irreducibility Theorem (1995) (15)
On a problem in elementary number theory (1992) (15)
Involutive Heegaard Floer homology and rational cuspidal curves (2016) (14)
On sums of powers of the positive integers (2013) (14)
Reducibility of lacunary polynomials, VI (1986) (14)
On the least prime primitive root modulo a prime (2002) (14)
On a decomposition of polynomials in several variables (2002) (13)
A decomposition of integer vectors. IV (1991) (13)
On Hilbert's irreducibility theorem (1965) (13)
On equal values of trinomials (2011) (13)
On the factors of Stern polynomials (2011) (13)
Quadratic Diophantine equations with a parameter (1966) (13)
On sums of three unit fractions with polynomial denominators (2000) (13)
On the least integers represented by the genera of binary quadratic forms (1971) (13)
On interesting walks in a graph (1972) (12)
Multiplicative properties of the partition function (1987) (12)
On the representation of fields as finite unions of subfields (1959) (11)
Class Numbers and Short Sums of Kronecker Symbols (1999) (11)
On a problem of Lehmer (1983) (11)
Comparison of L^1- and L^infty -norms of squares of polynomials (2002) (11)
Stern Polynomials as Numerators of Continued Fractions (2014) (11)
Reducibility of polynomials of the form f(x)-g(y) (1967) (11)
On integers not of the form n - φ (n) (1995) (11)
Hasse's principle for systems of ternary quadratic forms and for one biquadratic form (1983) (11)
Sieve Methods, Exponential Sums, and their Applications in Number Theory: Squarefree Values of Polynomials and the abc-Conjecture (1997) (11)
A note on some properties of the functions φ (n), σ(n) and θ(n) (1958) (10)
On A Conjecture of Posner and Rumsey (1994) (10)
On a theorem of Bauer and some of its applications (1966) (10)
Addendum to the paper "On the product of the conjugates outside the unit circle of an algebraic number" (1975) (10)
Remarks on maximum and minimum exponents in factoring (1994) (10)
Class number of real Abelian fields (2015) (10)
On the reduced length of a polynomial with real coefficients (2007) (10)
On the greatest common divisor of two univariate polynomials, II (2001) (9)
On values of the Mahler measure in a quadratic field (solution of a problem of Dixon and Dubickas) (2004) (9)
On Vectors whose Span Contains a Given Linear Subspace (2005) (9)
Numerical calculation of the density of prime numbers with a given least primitive root (2002) (9)
Journées Arithmétiques 1980: Diophantine equations with parameters (1982) (9)
A remark on a paper of Bateman and Horn (1963) (9)
A note on certain arithmetical constants (1966) (9)
Integer points on conics (1972) (8)
Primitive roots and quadratic non-residues (2011) (8)
Reducibility of lacunary polynomials, VIII (1988) (8)
On the greatest prime factor of $prod^{x}_{k=1}f(k)$ (1990) (8)
On equations y^2=x^n+k in a finite field (2004) (8)
Admissible tracks in Shamir's scheme (2010) (8)
Multiplicative properties of sets of residues (2010) (7)
Self-inversive polynomials of odd degree (2007) (7)
On the number of irreducible factors of a polynomial II (1983) (7)
Equal values of trinomials revisited (2012) (7)
Multiplicative properties of sets of positive integers (2009) (7)
On Lucas and Lehmer sequences and their applications to Diophantine equations (1981) (7)
On the relation between two conjectures on polynomials (1980) (7)
On power residues (1975) (7)
TRIPLES OF POSITIVE INTEGERS WITH THE SAME SUM AND THE SAME PRODUCT (1996) (7)
Wacław Sierpinski's papers on the theory of numbers (1972) (7)
An application of Kloosterman sums (1995) (6)
Addendum and corrigendum to the paper "Abelian binomials, power residues and exponential congruences", Acta Arith. 32(1977), pp. 245-274 (1980) (6)
An extension of the theorem of Bauer and polynomials of certain special types (1966) (6)
On two conjectures of P. Chowla and S. Chowla concerning continued fractions (1974) (6)
Elementary symmetric polynomials in Shamir's scheme (2010) (6)
Diophantine approximation and sums of roots of unity (1967) (5)
On an analytic problem considered by Sierpi'nski and Ramanujan (1991) (5)
A property of the unitary convolution (1998) (5)
REDUCIBILITY OF POLYNOMIALS by (2010) (5)
On sums of roots of unity (Solution of two problems of R. M. Robinson) (1966) (5)
The reduced length of a polynomial with complex coefficients (2008) (5)
Reducibility of lacunary polynomials. X (1989) (5)
The Leading Coefficients of Stern Polynomials (2016) (5)
Reducibility of lacunary polynomials, V (1984) (5)
An extension of the theorem on primitive divisors in algebraic number fields (1993) (5)
On Lucas pseudoprimes with a prescribed value of the Jacobi symbol (2000) (5)
Reducibility of lacunary polynomials, VII (1986) (5)
Distributions of the values of some arithmetical functions (1961) (5)
On Homogeneous Covering Congruences (1997) (5)
On a decomposition of polynomials in several variables, II (2002) (4)
Corrigendum to the papers "On two theorems of Gelfond and some of their applications" and "On primitive prime factors of Lehmer numbers III" (1969) (4)
An Analog of Hilbert's Irreducibility Theorem (1990) (4)
Reducibility of Symmetric Polynomials (2005) (4)
On the Mahler measure of polynomials in many variables (1997) (4)
ON THE CONGRUENCE un ≡ c (mod p),WHERE un IS A RECURRING SEQUENCE OF THE SECOND ORDER (2003) (4)
A Panorama in Number Theory or The View from Baker's Garden: On the Greatest Common Divisor of Two Univariate Polynomials, I (2002) (4)
AN ANALOGUE OF HARNACK'S INEQUALITY FOR DISCRETE SUPERHARMONIC FUNCTIONS (1978) (4)
Elementary and analytic number theory (1999) (4)
On Expressible Sets of Geometric Sequences (2008) (4)
Extreme binary forms (2010) (4)
Solved and unsolved problems οn polynomials (1995) (4)
A NOTE ON ERDŐS–STRAUS AND ERDŐS–GRAHAM DIVISIBILITY PROBLEMS (WITH AN APPENDIX BY ANDRZEJ SCHINZEL) (2013) (4)
Zeta functions and the equivalence of integral forms. (1979) (3)
Diophantine problems and polynomials (1999) (3)
The Number of Solutions of a Linear Homogeneous Congruence (2008) (3)
On reducible trinomials. II. (2000) (3)
Reducibility of lacunary polynomials, IV (1984) (3)
Reducibility of lacunary polynomials, XI (1991) (3)
On Fixed Divisors of Forms in Many Variables, I (2014) (2)
On a linear homogeneous congruence (2006) (2)
Distribution of solutions of diophantine equations f1(x1)f2(x2) = f3(x3), where fi are polynomials (2018) (2)
The fundamental lemma of Brun's sieve in a new setting (1985) (2)
A note on the paper "Reducibility of lacunary polynomials I" (1971) (2)
The mathematical work of Eduard Wirsing (2006) (2)
On certain biquadratic equations (2013) (2)
Distribution of solutions of diophantine equations $f_1(x_1)f_2(x_2) = f_3(x_3)$, where $f_i$ are polynomials. - II (1994) (2)
On Sums of Four Coprime Squares (2013) (2)
Polynomials dertermined by a few of their coefficients (2004) (2)
Errata to "On reducible trinomials" (Dissertationes Mathematicae 329 (1993)) (1995) (2)
Corrigendum and addendum to the paper ``Reducibility of quadrinomials (2001) (2)
A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof) (2013) (2)
Elementary, analytic and geometric number theory (2007) (2)
Systems of Exponential Congruences (1985) (2)
On reducible trinomials, IV (2011) (2)
On the number of terms of a power of a polynomial (2009) (2)
The number of zeros of polynomials in valuation rings of complete discretely valued fields (1984) (2)
Erdős’s Work on the Sum of Divisors Function and on Euler’s Function (2013) (2)
An application of Hilbert's irreducibility theorem to diophantine equations (1982) (1)
Corrigendum to the paper "The mathematical work of Eduard Wirsing" Functiones et Approximatio 35 (2006), 7-18 (2006) (1)
Reducibility of a special symmetric form (2006) (1)
On the diophantine equation $x^2+x+1=yz$ (2015) (1)
On Ternary Integral Recurrences (2015) (1)
On the Diophantine equation $x^p+y^{2p}=z^2$ (1987) (1)
Concerning the characterization of linear spaces (1964) (1)
On the metric theory of continued fractions (1998) (1)
Powers of roots in linear spaces (2009) (1)
Corrigendum to the paper “Reducibility of lacunary polynomials XII” Acta Arith. 90 (1999), 273–289 (2019) (1)
A class of polynomials (1991) (1)
On the congruence f(x)+g(y)+c≡0 (mod xy) (completion of Mordell's proof) (2015) (1)
On the factors of Stern polynomials II. Proof of a conjecture of M. Gawron (2017) (1)
On Sums of Four Cubes of Polynomials (1968) (1)
A non-standard metric in the group of reals (1986) (1)
Polynomials with Special Regard to Reducibility: Polynomials over an algebraically closed field (2000) (1)
Extensions of Three Theorems of Nagell (2013) (1)
Families of curves having each an integer point (1982) (1)
On Simple Linear Recurrences (2017) (1)
THE RAMSEY-TYPE VERSION OF A PROBLEM OF POMERANCE AND SCHINZEL (2011) (0)
Theory of number in Paul Erdös' papers (2013) (0)
The reduced length of a polynomial with complex or real coefficients (Analytic Number Theory and Related Areas) (2009) (0)
The work of Władysław Narkiewicz in number theory and related areas (2008) (0)
Index: Authors of Abstracts (2016) (0)
THE NUMBER OF NON-ZERO COEFFICIENTS OF A POLYNOMIAL-SOLVED AND UNSOLVED PROBLEMS (2009) (0)
On the composite Lehmer numbers with prime indices, I (2017) (0)
Local-global principles for recurrence sequences (2019) (0)
Arbitrary polynomials over an arbitrary field (2000) (0)
Corrigenda to the paper "The number of zeros of polynomials in valuation rings of complete discretely valued fields" (Fund. Math. 124 (1984), 41-97) (2010) (0)
Polynomials with Special Regard to Reducibility: Appendices (2000) (0)
On some open problems of number theory (2018) (0)
JERZY URBANOWICZ'S WORK IN PURE MATHEMATICS (2013) (0)
Corrigendum to the paper "On the arithmetical theory of continued fractions,II", Acta Arith.7 (1962), pp. 287-298 (1986) (0)
Polynomials with Special Regard to Reducibility: Polynomials over a Kroneckerian field (2000) (0)
Solution to a Problem of Lubelski and an Improvement of a Theorem of His (2011) (0)
Sums and Products (2018) (0)
An improvement of a lemma from Gauss’s first proof of quadratic reciprocity (2017) (0)
On the number of terms in the irreducible factors of a polynomial over ℚ (1992) (0)
Corrigendum to the paper "On the greatest common divisor of two univariate polynomials, II" (Acta Arith. 98 (2001), 95-106) (2004) (0)
Prime factors of values of polynomials (2011) (0)
On a Linear Diophantine Equation (2013) (0)
On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (2016) (0)
Note to the Paper ``A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)'' (Bull. Polish Acad. Sci. Math. 61 (2013), 23–26) (2013) (0)
The congruence $f(x) + g(y) + c = 0$ $(mod$ $xy)$ (2014) (0)
Number Theory in Progress: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997 (1999) (0)
Index: Authors of Abstracts (2017) (0)
Corrigendum to the paper "On a theorem of Bauer and some of its applications" (Acta Arithmetica 11 (1966), pp. 333-344) (1967) (0)
On the congruence $f(x)+g(y)+c\equiv 0\ ({\rm mod}\ xy)$, II (the quadratic case) (2018) (0)
A remark on a paper of T. W. Cusick (1999) (0)
Corrigendum to "A note on some properties of the functions φ(n), σ(n) and θ(n)'' by A. Schinzel and Y. Wang (these Annales 4 (1958)) (1967) (0)
Polynomials with Special Regard to Reducibility: Lacunary polynomials over an arbitrary field (2000) (0)
Reducibility of polynomials over Kroneckerian fields (1998) (0)
On certain biquadratic equations, II (2018) (0)
Hooley, C., Applications of Sieve Methods to the Theory of Numbers. Cambridge‐London‐New York‐Melbourne. Cambridge University Press. 1976. 122 S., £ 7.25 A. (Cambridge Tracts in Mathematics 70.) (1978) (0)
A Remark on a Paper of Mordell (1969) (0)
Corrigendum to Two problems concerning polynomials (1965) (0)
Polynomials over a finitely generated field (2000) (0)
Equal values of trinomials revisited (2012) (0)
The modular distribution of Stern’s sequence (2019) (0)
Sums Involving the Hurwitz Zeta-Function Values (2005) (0)
On certain biquadratic equations (2013) (0)
A CONTRIBUTION TO COMBINATORIAL GEOMETRY (1973) (0)
The reduced length of a polynomial with complex or real coefficients (解析的整数論とその周辺--RIMS研究集会報告集) (2009) (0)
Sierpinski's contribution to the number theory (2014) (0)
Multiplicative properties of sets of residues C . (2011) (0)
On weak automorphs of binary forms over an arbitrary field (2005) (0)
DIFFERENCES BETWEEN VALUES OF A QUADRATIC FORM (1992) (0)
The Infinity in Mathematics (2008) (0)
Exponential congruences (Number Theory and its Applications) (1998) (0)
On the smallest number of terms of vanishing sums of units in number fields (2018) (0)
Addendum to the paper:"On two theorems of Gelfond and some of their applications" (Acta Arith. 13 (1967), pp. 177-236) (1990) (0)
Reciprocal Stern Polynomials (2015) (0)

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What Schools Are Affiliated With Andrzej Schinzel?

Andrzej Schinzel is affiliated with the following schools:

University of Warsaw

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