Melvyn B. Nathanson

Melvyn B. Nathanson's AcademicInfluence.com Rankings

Melvyn B. Nathanson

Mathematics

#426

World Rank

#858

Historical Rank

#192

USA Rank

Measure Theory

#717

World Rank

#966

Historical Rank

#285

USA Rank

mathematics Degrees

Download Badge

Mathematics

Why Is Melvyn B. Nathanson Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Melvyn Bernard Nathanson is an American mathematician, specializing in number theory, and a Professor of Mathematics at Lehman College and The Graduate Center . His principal work is in additive and combinatorial number theory. He is the author of over 200 research papers in mathematics, and author or editor of 27 books.

(See a Problem?)

Melvyn B. Nathanson'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

Additive Number Theory: Inverse Problems and the Geometry of Sumsets (1996) (588)
Elementary Methods in Number Theory (1999) (336)
Additive Number Theory (1996) (314)
Additive Number Theory The Classical Bases (1996) (289)
The Polynomial Method and Restricted Sums of Congruence Classes (1996) (158)
Waring’s problem for cubes (1996) (115)
Adding Distinct Congruence Classes Modulo a Prime (1995) (108)
Convexity and Sumsets (2000) (93)
On sums and products of integers (1997) (79)
Minimal bases and maximal nonbases in additive number theory (1974) (54)
SETS WITH MORE SUMS THAN DIFFERENCES (2006) (45)
Problems in additive number theory, I (2006) (45)
Unique representation bases for the integers (2002) (42)
Sums of Finite Sets of Integers (1972) (38)
Every function is the representation function of an additive basis for the integers (2003) (30)
Approximation by continued fractions (1974) (30)
Representation functions of sequences in additive number theory (1978) (29)
Desperately seeking mathematical truth (2008) (28)
Connected components of arithmetic graphs (1980) (25)
Minimal bases and powers of 2 (1988) (24)
Affine invariants, relatively prime sets, and a phi function for subsets of . (2007) (24)
PROBLEMS IN ADDITIVE NUMBER THEORY, IV: NETS IN GROUPS AND SHORTEST LENGTH g-ADIC REPRESENTATIONS (2011) (24)
Polynomial Pell’s equations (1976) (24)
Permutations, Periodicity, and Chaos (1977) (23)
A short proof of Cauchy’s polygonal number theorem (1987) (23)
A simple construction of minimal asymptotic bases (1989) (23)
Inverse theorems for subset sums (1995) (22)
Cofinite subsets of asymptotic bases for the positive integers (1985) (22)
A functional equation arising from multiplication of quantum integers (2002) (22)
Inverse problems for linear forms over finite sets of integers (2007) (22)
Quantum integers and cyclotomy (2003) (21)
Lagrange's Theorem and Thin Subsequences of Squares (1981) (21)
Oscillations of bases for the natural numbers (1975) (20)
Polynomial growth of sumsets in abelian semigroups (2002) (20)
Eastern Europe and the Soviet Union (1979) (19)
Weyl’s inequality (1996) (19)
Binary linear forms over finite sets of integers (2007) (18)
Inverse theorems and the number of sums and products (1999) (18)
Sumsets Contained in Infinite Sets of Integers (1980) (18)
The inverse problem for representation functions of additive bases (2003) (17)
Growth of Sumsets in Abelian Semigroups (2000) (17)
A new upper bound for finite additive bases (2005) (17)
A Mock Theta Function for the Delta-function (2009) (17)
Sumsets containing long arithmetic progressions and powers of 2 (1989) (17)
Derivatives of Binary Sequences (1971) (17)
Systems of distinct representatives and minimal bases in additive number theory (1979) (17)
Geometric group theory and arithmetic diameter (2011) (17)
Waring's problem for sets of density zero (1981) (16)
Additive number theory and the ring of quantum integers (2002) (16)
The Caccetta-Haggkvist conjecture and additive number theory (2006) (15)
Quadratic addition rules for quantum integers (2005) (14)
Arithmetic Progressions Contained in Sequences with Bounded Gaps (1980) (14)
The exact order of subsets of additive bases (1984) (14)
Additive number theory : festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson (2010) (14)
Representation functions of additive bases for abelian semigroups (2002) (13)
Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n} (2007) (13)
Lagrange’s theorem with ^{1/3} squares (1980) (13)
Problems and results on minimal bases in additive number theory (1987) (12)
Formal power series arising from multiplication of quantum integers (2003) (12)
A problem of Rankin on sets without geometric progressions (2014) (12)
Perfect difference sets constructed from Sidon sets (2006) (12)
On a problem of Rohrbach for finite groups (1992) (12)
s-Maximal Nonbases of Density Zero (1977) (12)
Piecewise linear functions with almost all points eventually periodic (1976) (11)
Linear Forms in Finite Sets of Integers (1998) (11)
Partitions of the natural numbers into infinitely oscillating bases and nonbases (1976) (11)
A forest of linear fractional transformations (2013) (11)
Number Theory and Semigroups of Intermediate Growth (1999) (11)
Number Theory Carbondale 1979 (1979) (11)
Irrational Numbers Associated to Sequences Without Geometric Progressions (2013) (10)
Desperately Seeking Mathematical Proof (2009) (10)
Additive Systems and a Theorem of de Bruijn (2013) (10)
Partitions with parts in a finite set (2000) (10)
NONBASES OF DENSITY ZERO NOT CONTAINED IN MAXIMAL NONBASES (1977) (10)
Problems in additive number theory, III (2009) (10)
Minimal asymptotic bases with prescribed densities (1988) (9)
Minimal Asymptotic Bases for the Natural Numbers (1980) (9)
Partial products in finite groups (1976) (9)
Cantor polynomials for semigroup sectors (2013) (9)
Dense sets of integers with prescribed representation functions (2007) (9)
Small Sets Satisfying the Central Sets Theorem (2009) (9)
Number Theory: New York Seminar 1991-1995 (1996) (9)
Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory (2008) (9)
Linear recurrences and uniform distribution (1975) (9)
Heights in finite projective space, and a problem on directed graphs (2007) (9)
Density of sets of natural numbers and the Lévy group (2006) (8)
On the maximum density of minimal asymptotic bases (1989) (8)
Sumsets Containing Infinite Arithmetic Progressions (1988) (8)
Pairs of Matrices in GL2(R≥0) That Freely Generate (2015) (8)
Generalized additive bases, Knig's lemma, and the ErdosTurn conjecture (2003) (8)
Sets of natural numbers with no minimal asymptotic bases (1978) (8)
HEIGHTS ON THE FINITE PROJECTIVE LINE (2007) (8)
Dirichlet L-Functions (1993) (8)
The Finite Heine Transformation (2009) (8)
Catalan's Equation in K(t) (1974) (8)
Asymptotic Density and the Asymptotics of Partition Functions (2000) (7)
Oscillations of bases in number theory and combinatorics (1977) (7)
On Sequences without Geometric Progressions (2013) (7)
Partitions of bases into disjoint unions of bases (1988) (7)
On Erdos's elementary method in the asymptotic theory of partitions (2000) (7)
Inverse Problems for Representation Functions in Additive Number Theory (2007) (7)
The Method of I.M. Vinogradov in the Theory of the Zeta Function (1993) (6)
On the Greatest Order of an Element of the Symmetric Group (1972) (6)
Simultaneous systems of representatives for families of finite sets (1988) (6)
MSTD sets and Freiman isomorphisms (2016) (6)
Mellin's formula and some combinatorial identities (1976) (6)
Complementing sets of $n$-tuples of integers (1972) (6)
Cantor Polynomials and the Fueter-Pólya Theorem (2015) (6)
Combinatorial number theory : proceedings of the 'Integers Conference 2005' in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, October 27-30, 2005 (2007) (5)
Difference operators and periodic sequences over finite modules (1976) (5)
Best Possible Results on the Density of Sumsets (1990) (5)
Bi-Lipschitz equivalent metrics on groups, and a problem in additive number theory (2009) (5)
Representation functions of bases for binary linear forms (2007) (5)
Every finite subset of an abelian group is an asymptotic approximate group (2015) (5)
An Inverse Problem in Number Theory and Geometric Group Theory (2009) (5)
Linear quantum addition rules (2006) (5)
Multiplicative representations of integers (1987) (5)
On a Partition Problem of Canfield and Wilf (2011) (5)
Additive problems in combinatorial number theory (1989) (5)
Alternate minimization and doubly stochastic matrices (2018) (5)
Multiplication rules for polynomials (1978) (4)
A Generalization of the Goldbach-Shnirel'man Theorem (1987) (4)
Classification problems in K-categories (1980) (4)
Bases and Nonbases of Square-Free Integers (1979) (4)
Cassels bases (2009) (4)
An Exponential Congruence of Mahler (1972) (4)
Problems in additive number theory, II: Linear forms and complementing sets (2009) (4)
Independence of solution sets and minimal asymptotic bases (1995) (4)
Assignments for the Benefit of Creditors (1957) (4)
Limits and Decomposition of de Bruijn’s Additive Systems (2013) (4)
Chen’s theorem (1996) (4)
On the Density of Integral Sets with Missing Differences (2009) (4)
Round Metric Spaces (1975) (4)
Sums and Differences of the Coordinates of Points on Modular Hyperbolas (2009) (4)
Dirichlet series of integers with missing digits (2020) (3)
Free monoids and forests of rational numbers (2014) (3)
Independence of Solution Sets in Additive Number Theory (1986) (3)
Frobenius Numbers of Generalized Fibonacci Semigroups (2009) (3)
Number theory : New York seminar 1989-1990 (1991) (3)
Curious convergent series of integers with missing digits (2020) (3)
A tree of linear fractional transformations (2013) (3)
Supersequences, rearrangements of sequences, and the spectrum of bases in additive number theory (2008) (3)
Matrix scaling, explicit Sinkhorn limits, and arithmetic (2019) (3)
On the Fractional Parts of Roots of Positive Real Numbers (2011) (3)
It seems I am a Jew : a Samizdat essay (1980) (3)
Finite Graphs and the Number of Sums and Products (1996) (3)
Problems in additive number theory, V: Affinely inequivalent MSTD sets (2016) (3)
On the ubiquity of Sidon sets (2003) (3)
Integrals of Binary Sequences (1972) (3)
Matrix scaling and explicit doubly stochastic limits (2019) (3)
Sums of Finite Sets of Integers, II (2020) (3)
Pick's theorem and sums of lattice points (2015) (3)
105.06 The Hermite-Sylvester criterion for real-rooted polynomials (2019) (3)
Asymptotic distribution and asymptotic independence of sequences of integers (1977) (3)
Every finite set of integers is an asymptotic approximate group (2015) (2)
One, Two, Many: Individuality and Collectivity in Mathematics (2011) (2)
Sidon sets for linear forms (2021) (2)
On the fundamental domain of a discrete group (1973) (2)
On a diophantine equation of Muneer (2016) (2)
An Elementary Proof for the Krull Dimension of a Polynomial Ring (2016) (2)
Products of Sums of Powers (1975) (2)
Simultaneous systems of representatives and combinatorial number theory (1990) (2)
Interactions of zeros of polynomials and multiplicity matrices (2022) (2)
Thin bases in additive number theory (2012) (2)
Largest and smallest maximal sets of pairwise disjoint partitions (1983) (2)
An algorithm for partitions (1975) (2)
Paul Erdős and additive bases (2014) (2)
Forests of complex numbers (2014) (2)
Combinatorial and Additive Number Theory IV (2021) (2)
Additive bases with many representations (1989) (2)
Information Minimisation, Markov Transition, and Dynamic Modelling (1978) (2)
Sums of products of congruence classes and of arithmetic progressions (2007) (2)
Komar/Melamid: Two Soviet Dissident Artists (1980) (2)
Sumsets containing k-free integers (1989) (2)
On the Sum of the Reciprocals of the Differences Between Consecutive Primes (1996) (2)
Nets in groups, minimum length $g$-adic representations, and minimal additive complements (2008) (2)
Number Theory Day (1977) (2)
ADDITIVE h‐BASES FOR LATTICE POINTS 1 (1979) (2)
The Erdős Paradox (2015) (2)
Waring’s problem for finite intervals (1986) (2)
The Haight-Ruzsa method for sets with more differences than multiple sums (2016) (2)
Prime Polynomial Sequences (1976) (2)
N-graphs, Modular Sidon and Sum-Free Sets, and Partition Identities (2000) (2)
Column-to-Row Operations on Partitions: The Envelopes (2009) (2)
Who Owns the Theorem? (2020) (1)
Shatrovskii's construction of thin bases (2009) (1)
Sumsets of measurable sets (1980) (1)
The Simplest Inverse Problems in Additive Number Theory (2017) (1)
Matrix Scaling Limits in Finitely Many Iterations (2018) (1)
Sums of Polygonal Numbers (1987) (1)
Growth Polynomials for Additive Quadruples and (h, k)-Tuples (2013) (1)
Continuity of the roots of a polynomial (2022) (1)
Finitely generated and not finitely generated rings (2016) (1)
An extremal problem for least common multiples (1987) (1)
The Muirhead-Rado inequality, 2: Symmetric means and inequalities (2022) (1)
Sumsets contained in sets of upper Banach density 1 (2015) (1)
The Bose-Chowla argument for Sidon sets (2021) (1)
Comparison estimates for linear forms in additive number theory (2016) (1)
Addictive Number Theory (2010) (1)
Pairs of matrices in $GL_2(\mathbf{R}_{\geq 0})$ that freely generate (2014) (1)
Linear forms and complementing sets of integers (2008) (1)
Number theory : New York seminar, 2003 (2003) (1)
Geometric progressions in syndetic sets (2020) (1)
SEMIDIRECT PRODUCTS AND FUNCTIONAL EQUATIONS FOR QUANTUM MULTIPLICATION (2006) (1)
Weighted real Egyptian numbers (2017) (1)
An inverse problem for finite Sidon sets (2021) (1)
An Inverse Theorem for Sums of Sets of Lattice Points (1994) (1)
Trapezoidal numbers, divisor functions, and a partition theorem of Sylvester (2016) (1)
On the Euler Product of Some Zeta Functions (2009) (1)
MULTIPLICATIVE PROOFS OF SOME GENERALIZATIONS OF MENON’S IDENTITY (2021) (1)
Soviet reactors to open for international inspection (1985) (1)
Unusual Applications of Number Theory (2004) (1)
Maximal Sidon sets and matroids (2005) (1)
Elementary calculation of the dimensions of some monomial varieties (2016) (1)
Shift dynamical systems over finite fields (1972) (1)
The Muirhead-Rado inequality, 1 Vector majorization and the permutohedron (2021) (1)
Gauss's proof of Descartes's rule of signs (2022) (1)
Underapproximation by Egyptian fractions (2022) (1)
Sums of three primes (1996) (1)
Exploring platform (semi)groups for non-commutative key-exchange protocols (2017) (1)
Additive Number Theory and Linear Semigroups with Intermediate Growth (2014) (0)
The Euler Gamma Function (1993) (0)
Multiplicative Representations of Integers and Ramsey’s Theorem (2020) (0)
Patterns in the iteration of an arithmetic function (2022) (0)
Convergent and divergent series of integers with missing digits (2020) (0)
Generalizations of Menon's arithmetic identity (2021) (0)
Gauss: A Biographical Study, W. K. Bühler (1982) (0)
Sums of polygons (1996) (0)
Not All Groups Are LEF Groups, or Can You Know If a Group Is Infinite? (2018) (0)
MAXIMAL ASYMPTOTIC NONBASES PAUL ERDiiS AND (1975) (0)
The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals (1993) (0)
Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture (2013) (0)
Infinite sumsets with many representations (2014) (0)
Monomial congruences (1978) (0)
Two Applications of Combinatorics to Number Theory (1989) (0)
Growth Polynomials for Additive Quadruples and (h, k)-Tuples (2014) (0)
The Connection Between the Sum of the Coefficients of a Dirichlet Series and the Function Defined by this Series (1993) (0)
Arithmetic functions and fixed points of powers of permutations (2022) (0)
Combinatorics of Ramanujan–Slater Type Identities (2009) (0)
Adjoining identities and zeros to semigroups (2006) (0)
Self Generating Sets and Numeration Systems (2009) (0)
A nonstandard proof of continuity of affine varieties (2022) (0)
Decomposition and limits of de Bruijn's additive systems (2013) (0)
Sums of sets of lattice points and unimodular coverings of polytopes (2015) (0)
Essential Components in Discrete Groups (1975) (0)
Descartes's"Rule of Signs'' and Poincar\'e's Positivstellensatz (2022) (0)
(ii)' limm g=m, u(Ak) = O uniformly for j _ 1 and {A I} 5 E disjoint. The example above shows that these results are false for strongly bounded set functions defined on algebras, although (2016) (0)
Families of linear semigroups with intermediate growth (2006) (0)
Decomposing sequences into monotonic subsequences (2006) (0)
Convergent series of integers with missing digits (2020) (0)
Entire Functions of Finite Order (1993) (0)
Controlling Science Information (1985) (0)
The Shnirel’man-Goldbach theorem (1996) (0)
On a diophantine equation of M. J. Karama (2016) (0)
Divisibility properties of additive bases (1986) (0)
Combinatorial Pairs, and Sumsets Contained in Sequences (1989) (0)
Subalgebras of a Polynomial Ring That Are Not Finitely Generated (2017) (0)
Convergent series of integers with missing digits (2021) (0)
A curious convergent series. (2020) (0)
Polytopes, polyhedra, and the Farkas lemma (2022) (0)
OSCILLATIONS OF BASES FOR THE NATURAL NUMBERS 255 Proof (1975) (0)
Congruence classes and maximal nonbases (2020) (0)
Bases in finite groups of small order (2021) (0)
The Hardy—Littlewood asymptotic formula (1996) (0)
Prime Numbers in Arithmetic Progressions (1993) (0)
Adding distinct residue classes modulo a prime (DRAFT) (2002) (0)
FIXED POINTS OF POWERS OF PERMUTATIONS (2022) (0)
Sums of sets of lattice points and unimodular coverings of polytopes (2016) (0)
A pr 2 00 2 Polynomial growth of sumsets in abelian semigroups ∗ (2008) (0)
Inverse Theorems for Subset Sums 1 (1994) (0)
Finding Almost Squares III (2009) (0)
Elementary estimates for primes (1996) (0)
Heron Sequences and Their Modifications (2009) (0)
Commutative Algebra and the Linear Diophantine Problem of Frobenius (2016) (0)
Orwell and the atom bomb (1984) (0)
Unusual applications of number theory : DIMACS Workshop, Unusual Applications of Number Theory, January 10-14, 2000, DIMACS Center (2004) (0)
DISTRIBUTION OF DIGITS IN PERIODIC DECIMALS (0)
of Integers Conference 2009 PHASE TRANSITIONS IN INFINITELY (0)
Long arithmetic progressions and powers of 2 (1989) (0)
Three Questions About John von Neumann (2023) (0)
1 2 Fe b 20 00 Growth of sumsets in abelian semigroups ∗ (2008) (0)
Publications of Ron L. Graham (2007) (0)
Real-rooted polynomials and a generalized Hermite-Sylvester theorem (2020) (0)
Maier Matrices Beyond Z (2009) (0)
Primitive sets and an Euler phi function for subsets of {1,2,...,n} (2006) (0)
Sinkhorn limits in finitely many steps (2019) (0)
Congruence classes and maximal nonbases (2020) (0)
Academic freedom versus nonproliferation: the Libyan case (1985) (0)
The Goldbach Conjecture (1993) (0)
Commuting translations and multiplications by powers (2020) (0)
Chromatic sumsets (2020) (0)
Tennenbaum at Penn and Rochester (2006) (0)
A new class of minimal asymptotic bases (2020) (0)
Sidon Sets and Perturbations (2017) (0)
The Hilbert-Waring theorem (1996) (0)
Exponential automorphisms and a problem of Mycielski (2022) (0)
Dimensions of Monomial Varieties (2016) (0)
Paul Erd\H os and additive bases (2014) (0)
Number theory day : proceedings of the conference held at Rockefeller University, New York, 1976 (1977) (0)
106.03 Real-rooted polynomials and a generalised Hermite-Sylvester theorem (2022) (0)
Combinatorial number theory : proceedings of the "Integers Conference 2011", Carrollton, Georgia, USA, October 26-29, 2011 (2009) (0)
Problems in Additive Number Theory, III: Thematic Seminars at the Centre de Recerca Matematica (2008) (0)
Combinatorial and additive number theory : CANT 2011 and 2012 (2014) (0)
Number theory, Carbondale 1979 : proceedings of the Southern Illinois Number Theory Conference, Carbondale, March 30 and 31, 1979 (1979) (0)
von Neumann-Steinhaus decomposition of an interval (2022) (0)
An American mathematician in Moscow, or how I destroyed the Soviet Union (2014) (0)
Linear Equations Involving Iterates of σ (N) (2009) (0)

This paper list is powered by the following services:

Other Resources About Melvyn B. Nathanson

en.wikipedia.org

What Schools Are Affiliated With Melvyn B. Nathanson?

Melvyn B. Nathanson is affiliated with the following schools:

Melvyn B. Nathanson's Academic­Influence.com Rankings