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## Nathanson, Melvyn Bernard

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 Author ID: nathanson.melvyn-bernard Published as: Nathanson, M. B.; Nathanson, Melvin B.; Nathanson, Melvyn; Nathanson, Melvyn B.; Nathanson, Melvyn Bernard Homepage: http://comet.lehman.cuny.edu/nathanson/ External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 216 Publications since 1971, including 24 Books Biographic References: 3 Publications
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#### Co-Authors

 148 single-authored 19 Erdős, Pál 8 Nešetřil, Jaroslav 7 Chudnovsky, David V. 7 Chudnovsky, Gregory V. 7 Pomerance, Carl Bernard 6 Landman, Bruce M. 5 Cohn, Harvey 5 Nowakowski, Richard J. 5 Ruzsa, Imre Z. 5 Sárközy, András 4 O’Bryant, Kevin 3 Alon, Noga M. 3 Jia, Xingde 3 Robertson, Aaron 2 Alladi, Krishnaswami 2 Cilleruelo, Javier 2 Kahane, Jean-Pierre 2 Krantz, Steven George 2 Orosz, Brooke 2 Tenenbaum, Gérald 1 Borisov, Alexander 1 Choi, S. L. G. 1 Chowla, Sarvadaman 1 Cohen, Alex 1 Cohen, Seth D. 1 Elekes, György 1 Garcia, Stephan Ramon 1 Goldston, Daniel Alan 1 Graham, Ronald Lewis 1 Granville, Andrew James 1 Güntürk, Cemalettin Sinan 1 Han, Shuping 1 Kirfel, Christoph 1 Kontorovich, Alex V. 1 Konyagin, Sergeĭ Vladimirovich 1 Levy, Karl 1 Ljujić, Željka 1 Lovász, László 1 Luca, Florian 1 Nash, John C. M. 1 Parikh, Rohit 1 Perdigão Dias da Silva, José António 1 Shoemaker, Amy L. 1 Silva, Manuel Americo G. 1 Solymosi, József 1 Sós, Vera Turán 1 Spencer, Joel H. 1 Sullivan, Blair D. 1 Szabados, Jozsef 1 Tetali, Prasad 1 Wang, Yang
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#### Serials

 22 Proceedings of the American Mathematical Society 21 Journal of Number Theory 15 American Mathematical Monthly 15 Integers 9 Acta Arithmetica 6 Lecture Notes in Mathematics 5 Discrete Mathematics 5 International Journal of Number Theory 4 Acta Mathematica Hungarica 3 Functiones et Approximatio. Commentarii Mathematici 3 Journal of the London Mathematical Society. Second Series 3 Monatshefte für Mathematik 3 Notices of the American Mathematical Society 3 Graduate Texts in Mathematics 3 Springer Proceedings in Mathematics & Statistics 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 The Mathematical Intelligencer 2 Journal of Combinatorial Theory. Series A 2 Linear Algebra and its Applications 2 SIAM Journal on Applied Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 The Ramanujan Journal 2 Portugaliae Mathematica. Nova Série 2 Journal of Algebra and its Applications 1 Discrete Applied Mathematics 1 Israel Journal of Mathematics 1 Mathematics Magazine 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Fundamenta Mathematicae 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Publicationes Mathematicae 1 Semigroup Forum 1 Studia Scientiarum Mathematicarum Hungarica 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Combinatorica 1 Journal of the Ramanujan Mathematical Society 1 European Mathematical Society Newsletter 1 CRM Proceedings & Lecture Notes 1 DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 1 Moscow Journal of Combinatorics and Number Theory 1 Palestine Journal of Mathematics 1 North-Western European Journal of Mathematics 1 De Gruyter Proceedings in Mathematics
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#### Fields

 185 Number theory (11-XX) 45 Combinatorics (05-XX) 25 General and overarching topics; collections (00-XX) 21 Group theory and generalizations (20-XX) 10 Field theory and polynomials (12-XX) 8 History and biography (01-XX) 7 Difference and functional equations (39-XX) 4 Commutative algebra (13-XX) 4 Algebraic geometry (14-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 General topology (54-XX) 3 Convex and discrete geometry (52-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Geometry (51-XX) 2 Computer science (68-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

130 Publications have been cited 896 times in 647 Documents Cited by Year
Additive number theory. Inverse problems and the geometry of sumsets. Zbl 0859.11003
Nathanson, Melvyn B.
1996
Additive number theory. The classical bases. Zbl 0859.11002
Nathanson, Melvyn B.
1996
Elementary methods in number theory. Zbl 0953.11002
Nathanson, Melvyn B.
2000
The polynomial method and restricted sums of congruence classes. Zbl 0861.11006
Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre
1996
Adding distinct congruence classes modulo a prime. Zbl 0849.11081
Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre
1995
Convexity and sumsets. Zbl 0998.11010
Elekes, György; Nathanson, Melvyn B.; Ruzsa, Imre Z.
2000
Minimal bases and maximal nonbases in additive number theory. Zbl 0287.10051
Nathanson, Melvyn B.
1974
On sums and products of integers. Zbl 0869.11010
Nathanson, Melvyn B.
1997
Problems in additive number theory. I. Zbl 1183.11006
Nathanson, Melvyn B.
2007
Additive number theory and the ring of quantum integers. Zbl 1158.11303
Nathanson, M. B.
2006
Sets with more sums than differences. Zbl 1107.11017
Nathanson, Melvyn B.
2007
Unique representation bases for the integers. Zbl 1154.11306
Nathanson, Melvyn B.
2003
Partial products in finite groups. Zbl 0344.20024
Nathanson, Melvyn B.
1976
A functional equation arising from multiplication of quantum integers. Zbl 1055.39039
Nathanson, Melvyn B.
2003
Minimal bases and powers of 2. Zbl 0601.10040
Nathanson, Melvyn B.
1988
Sums of finite sets of integers. Zbl 0251.10002
Nathanson, Melvin B.
1972
Problems in additive number theory. IV: Nets in groups and shortest length $$g$$-adic representations. Zbl 1252.11007
Nathanson, Melvyn B.
2011
Inverse theorems for subset sums. Zbl 0835.11006
Nathanson, Melvyn B.
1995
A simple construction of minimal asymptotic bases. Zbl 0683.10043
Jia, Xingde; Nathanson, Melvyn B.
1989
Cofinite subsets of asymptotic bases for the positive integers. Zbl 0578.10056
Nash, John C. M.; Nathanson, Melvyn B.
1985
Representation functions of sequences in additive number theory. Zbl 0396.10045
Nathanson, Melvyn B.
1978
Quantum integers and cyclotomy. Zbl 1063.39020
Borisov, Alexander; Nathanson, Melvyn B.; Wang, Yang
2004
Sumsets containing long arithmetic progressions and powers of 2. Zbl 0693.10040
Nathanson, Melvyn B.; Sárközy, András
1989
Permutations, periodicity, and chaos. Zbl 0375.05002
Nathanson, Melvyn B.
1977
Perfect difference sets constructed from Sidon sets. Zbl 1199.11045
Cilleruelo, Javier; Nathanson, Melvyn B.
2008
Polynomial Pell’s equations. Zbl 0327.10021
Nathanson, Melvyn B.
1976
Oscillations of bases for the natural numbers. Zbl 0319.10066
Erdős, Paul; Nathanson, Melvyn B.
1975
Maximal asymptotic nonbases. Zbl 0296.10031
Erdős, Paul; Nathanson, Melvyn B.
1975
A forest of linear fractional transformations. Zbl 1390.11021
Nathanson, Melvyn B.
2015
A new upper bound for finite additive bases. Zbl 1157.11005
Güntürk, C. Sinan; Nathanson, Melvyn B.
2006
Formal power series arising from multiplication of quantum integers. Zbl 1066.39020
Nathanson, Melvyn B.
2004
Number theory and semigroups of intermediate growth. Zbl 0990.20037
Nathanson, Melvyn B.
1999
Inverse theorems and the number of sums and products. Zbl 0947.11008
Nathanson, Melvyn B.; Tenenbaum, Gérald
1999
On a problem of Rohrbach for finite groups. Zbl 0760.11003
Nathanson, Melvyn B.
1992
Sumsets contained in infinite sets of integers. Zbl 0451.10036
Nathanson, Melvyn B.
1980
Arithmetic progressions contained in sequences with bounded gaps. Zbl 0444.10053
Nathanson, Melvyn B.
1980
Approximation by continued fractions. Zbl 0293.10015
Nathanson, Melvyn B.
1974
Pairs of matrices in $$\mathrm{GL}_2(\mathbb R_{\geq 0})$$ that freely generate. Zbl 1358.20049
Nathanson, Melvyn B.
2015
Irrational numbers associated to sequences without geometric progressions. Zbl 1314.11011
Nathanson, Melvyn B.; O’Bryant, Kevin
2014
Dense sets of integers with prescribed representation functions. Zbl 1371.11017
Cilleruelo, Javier; Nathanson, Melvyn B.
2013
Cassels bases. Zbl 1256.11007
Nathanson, Melvyn B.
2010
Binary linear forms over finite sets of integers. Zbl 1156.11011
Nathanson, Melvyn B.; O’Bryant, Kevin; Orosz, Brooke; Ruzsa, Imre; Silva, Manuel
2007
Density of sets of natural numbers and the Lévy group. Zbl 1128.11006
Nathanson, Melvyn B.; Parikh, Rohit
2007
Kontorovich, Alex V.; Nathanson, Melvyn B.
2006
Every function is the representation function of an additive basis for the integers. Zbl 1133.11005
Nathanson, Melvyn B.
2005
Growth of sumsets in Abelian semigroups. Zbl 0959.20055
Nathanson, Melvyn B.
2000
Minimal asymptotic bases with prescribed densities. Zbl 0651.10035
Erdős, Paul; Nathanson, Melvyn B.
1988
Sumsets containing infinite arithmetic progressions. Zbl 0633.10047
Erdős, Paul; Nathanson, Melvyn B.; Sárközy, András
1988
Multiplicative representations of integers. Zbl 0621.10040
Nathanson, Melvyn B.
1987
s-maximal nonbases of density zero. Zbl 0345.10028
Nathanson, Melvyn B.
1977
Piecewise linear functions with almost all points eventually periodic. Zbl 0339.26008
Nathanson, Melvyn B.
1977
Matrix scaling and explicit doubly stochastic limits. Zbl 07099554
Nathanson, Melvyn B.
2019
On sequences without geometric progressions. Zbl 1330.11007
Nathanson, Melvyn B.; O’Bryant, Kevin
2013
Geometric group theory and arithmetic diameter. Zbl 1249.11017
Nathanson, Melvyn B.
2011
An inverse problem in number theory and geometric group theory. Zbl 1256.11054
Nathanson, Melvyn B.
2010
Inverse problems for linear forms over finite sets of integers. Zbl 1163.11067
Nathanson, Melvyn B.
2008
Generalized additive bases, König’s lemma, and the Erdős–Turán conjecture. Zbl 1090.11010
Nathanson, Melvyn B.
2004
Polynomial growth of sumsets in abelian semigroups. Zbl 1077.11014
Nathanson, Melvyn B.; Ruzsa, Imre Z.
2002
Partitions with parts in a finite set. Zbl 0969.11035
Nathanson, Melvyn B.
2000
Simultaneous systems of representatives for families of finite sets. Zbl 0709.05006
Nathanson, Melvyn B.
1988
A short proof of Cauchy’s polygonal number theorem. Zbl 0611.10036
Nathanson, Melvyn B.
1987
The exact order of subsets of additive bases. Zbl 0544.10058
Nathanson, Melvyn B.
1984
Lagrange’s theorem and thin subsequences of squares. Zbl 0539.10038
Erdős, Paul; Nathanson, Melvyn B.
1981
Systems of distinct representatives and minimal bases in additive number theory. Zbl 0414.10053
Erdős, Paul; Nathanson, Melvyn B.
1979
Multiplication rules for polynomials. Zbl 0392.39002
Nathanson, Melvyn B.
1978
Nonbases of density zero not contained in maximal nonbases. Zbl 0357.10029
Erdős, Paul; Nathanson, Melvyn B.
1977
Difference operators and periodic sequences over finite modules. Zbl 0344.12101
Nathanson, Melvyn B.
1976
Mellin’s formula and some combinatorial identities. Zbl 0343.05011
1976
Derivatives of binary sequences. Zbl 0257.68040
Nathanson, Melvyn B.
1971
MSTD sets and Freiman isomorphisms. Zbl 1418.11022
Nathanson, Melvyn B.
2018
Free monoids and forests of rational numbers. Zbl 1358.05056
Nathanson, Melvyn B.
2017
Every finite set of integers is an asymptotic approximate group. Zbl 1373.11007
Nathanson, Melvyn B.
2016
Reflections on Paul Erdős on his birth centenary. Zbl 1338.01020
Alladi, Krishnaswami (ed.); Krantz, Steven (ed.); Lóvasz, László; Sós, Vera T.; Graham, Ronald L.; Spencer, Joel; Kahane, Jean-Pierre; Nathanson, Melvyn B.
2015
A problem of Rankin on sets without geometric progressions. Zbl 1390.11025
Nathanson, Melvyn B.; O’Bryant, Kevin
2015
Phase transitions in infinitely generated groups, and related problems in additive number theory. Zbl 1261.11010
Nathanson, Melvyn B.
2011
The Caccetta-Häggkvist conjecture and additive number theory. Zbl 1184.05056
Nathanson, Melvyn B.
2009
Affine invariants, relatively prime sets, and a phi function for subsets of $$\{1, 2,\dots, n\}$$. Zbl 1114.11005
Nathanson, Melvyn B.
2007
Representation functions of additive bases for abelian semigroups. Zbl 1122.11006
Nathanson, Melvyn B.
2004
The inverse problem for representation functions of additive bases. Zbl 1130.11009
Nathanson, Melvyn B.
2004
Linear forms in finite sets of integers. Zbl 0911.11008
Han, Shu-Ping; Kirfel, Christoph; Nathanson, Melvyn B.
1998
The simplest inverse problems in additive number theory. Zbl 0804.11008
Nathanson, Melvyn B.
1993
Problems and results on minimal bases in additive number theory. Zbl 0622.10041
Erdős, Paul; Nathanson, Melvyn B.
1987
Waring’s problem for sets of density zero. Zbl 0476.10042
Nathanson, Melvyn B.
1981
Classification problems in K-categories. Zbl 0457.18007
Nathanson, Melvyn B.
1980
Lagrange’s theorem with $$N^{1/3}$$ squares. Zbl 0436.10024
Choi, S. L. G.; Erdős, Paul; Nathanson, Melvyn B.
1980
Minimal asymptotic bases for the natural numbers. Zbl 0426.10057
Erdős, Paul; Nathanson, Melvyn B.
1980
Sets of natural numbers with no minimal asymptotic bases. Zbl 0389.10038
Erdős, Paul; Nathanson, Melvyn B.
1978
Prime polynomial sequences. Zbl 0346.10027
Cohen, S. D.; Erdős, Paul; Nathanson, M. B.
1976
Partitions of the natural numbers into infinitely oscillating bases and nonbases. Zbl 0329.10045
Erdős, Paul; Nathanson, Melvyn B.
1976
Linear recurrences and uniform distribution. Zbl 0301.10032
Nathanson, Melvyn B.
1975
Catalan’s equation in K(t). Zbl 0282.10008
Nathanson, Melvyn B.
1974
Alternate minimization and doubly stochastic matrices. Zbl 1440.15039
Nathanson, Melvyn B.
2020
Weighted real Egyptian numbers. Zbl 1416.11050
Nathanson, Melvyn B.
2019
Pick’s theorem and sums of lattice points. Zbl 1400.52016
Levy, Karl; Nathanson, Melvyn B.
2018
An elementary proof for the Krull dimension of a polynomial ring. Zbl 1395.13008
Nathanson, Melvyn B.
2018
Every finite subset of an abelian group is an asymptotic approximate group. Zbl 1452.11015
Nathanson, Melvyn B.
2018
Sumsets contained in sets of upper Banach density 1. Zbl 1418.11016
Nathanson, Melvyn B.
2017
On a Diophantine equation of M. J. Karama. Zbl 1364.11080
Nathanson, Melvyn B.
2017
Forests of complex numbers. Zbl 1394.05010
Nathanson, Melvyn B.
2017
Cantor polynomials for semigroup sectors. Zbl 1290.05010
Nathanson, Melvyn B.
2014
Alternate minimization and doubly stochastic matrices. Zbl 1440.15039
Nathanson, Melvyn B.
2020
Matrix scaling and explicit doubly stochastic limits. Zbl 07099554
Nathanson, Melvyn B.
2019
Weighted real Egyptian numbers. Zbl 1416.11050
Nathanson, Melvyn B.
2019
MSTD sets and Freiman isomorphisms. Zbl 1418.11022
Nathanson, Melvyn B.
2018
Pick’s theorem and sums of lattice points. Zbl 1400.52016
Levy, Karl; Nathanson, Melvyn B.
2018
An elementary proof for the Krull dimension of a polynomial ring. Zbl 1395.13008
Nathanson, Melvyn B.
2018
Every finite subset of an abelian group is an asymptotic approximate group. Zbl 1452.11015
Nathanson, Melvyn B.
2018
Free monoids and forests of rational numbers. Zbl 1358.05056
Nathanson, Melvyn B.
2017
Sumsets contained in sets of upper Banach density 1. Zbl 1418.11016
Nathanson, Melvyn B.
2017
On a Diophantine equation of M. J. Karama. Zbl 1364.11080
Nathanson, Melvyn B.
2017
Forests of complex numbers. Zbl 1394.05010
Nathanson, Melvyn B.
2017
Every finite set of integers is an asymptotic approximate group. Zbl 1373.11007
Nathanson, Melvyn B.
2016
A forest of linear fractional transformations. Zbl 1390.11021
Nathanson, Melvyn B.
2015
Pairs of matrices in $$\mathrm{GL}_2(\mathbb R_{\geq 0})$$ that freely generate. Zbl 1358.20049
Nathanson, Melvyn B.
2015
Reflections on Paul Erdős on his birth centenary. Zbl 1338.01020
Alladi, Krishnaswami (ed.); Krantz, Steven (ed.); Lóvasz, László; Sós, Vera T.; Graham, Ronald L.; Spencer, Joel; Kahane, Jean-Pierre; Nathanson, Melvyn B.
2015
A problem of Rankin on sets without geometric progressions. Zbl 1390.11025
Nathanson, Melvyn B.; O’Bryant, Kevin
2015
Irrational numbers associated to sequences without geometric progressions. Zbl 1314.11011
Nathanson, Melvyn B.; O’Bryant, Kevin
2014
Cantor polynomials for semigroup sectors. Zbl 1290.05010
Nathanson, Melvyn B.
2014
Additive systems and a theorem of de Bruijn. Zbl 1373.11006
Nathanson, Melvyn B.
2014
Dense sets of integers with prescribed representation functions. Zbl 1371.11017
Cilleruelo, Javier; Nathanson, Melvyn B.
2013
On sequences without geometric progressions. Zbl 1330.11007
Nathanson, Melvyn B.; O’Bryant, Kevin
2013
On the fractional parts of roots of positive real numbers. Zbl 1305.11061
Nathanson, Melvyn B.
2013
On a partition problem of Canfield and Wilf. Zbl 1272.11111
Ljujić, Željka; Nathanson, Melvyn B.
2012
Problems in additive number theory. IV: Nets in groups and shortest length $$g$$-adic representations. Zbl 1252.11007
Nathanson, Melvyn B.
2011
Geometric group theory and arithmetic diameter. Zbl 1249.11017
Nathanson, Melvyn B.
2011
Phase transitions in infinitely generated groups, and related problems in additive number theory. Zbl 1261.11010
Nathanson, Melvyn B.
2011
Cassels bases. Zbl 1256.11007
Nathanson, Melvyn B.
2010
An inverse problem in number theory and geometric group theory. Zbl 1256.11054
Nathanson, Melvyn B.
2010
The Caccetta-Häggkvist conjecture and additive number theory. Zbl 1184.05056
Nathanson, Melvyn B.
2009
Problems in additive number theory. III. Zbl 1221.11023
Nathanson, Melvyn B.
2009
Problems in additive number theory. II: Linear forms and complementing sets. Zbl 1239.11025
Nathanson, Melvyn B.
2009
Desperately seeking mathematical proof. Zbl 1172.03004
Nathanson, Melvyn B.
2009
Heights on the finite projective line. Zbl 1177.11009
Nathanson, Melvyn B.
2009
Perfect difference sets constructed from Sidon sets. Zbl 1199.11045
Cilleruelo, Javier; Nathanson, Melvyn B.
2008
Inverse problems for linear forms over finite sets of integers. Zbl 1163.11067
Nathanson, Melvyn B.
2008
Inverse problems for representation functions in additive number theory. Zbl 1210.11107
Nathanson, Melvyn B.
2008
Heights in finite projective space, and a problem on directed graphs. Zbl 1177.11010
Nathanson, Melvyn B.; Sullivan, Blair D.
2008
Problems in additive number theory. I. Zbl 1183.11006
Nathanson, Melvyn B.
2007
Sets with more sums than differences. Zbl 1107.11017
Nathanson, Melvyn B.
2007
Binary linear forms over finite sets of integers. Zbl 1156.11011
Nathanson, Melvyn B.; O’Bryant, Kevin; Orosz, Brooke; Ruzsa, Imre; Silva, Manuel
2007
Density of sets of natural numbers and the Lévy group. Zbl 1128.11006
Nathanson, Melvyn B.; Parikh, Rohit
2007
Affine invariants, relatively prime sets, and a phi function for subsets of $$\{1, 2,\dots, n\}$$. Zbl 1114.11005
Nathanson, Melvyn B.
2007
Linear quantum addition rules. Zbl 1170.11005
Nathanson, Melvyn B.
2007
Additive number theory and the ring of quantum integers. Zbl 1158.11303
Nathanson, M. B.
2006
A new upper bound for finite additive bases. Zbl 1157.11005
Güntürk, C. Sinan; Nathanson, Melvyn B.
2006
Kontorovich, Alex V.; Nathanson, Melvyn B.
2006
Every function is the representation function of an additive basis for the integers. Zbl 1133.11005
Nathanson, Melvyn B.
2005
Quantum integers and cyclotomy. Zbl 1063.39020
Borisov, Alexander; Nathanson, Melvyn B.; Wang, Yang
2004
Formal power series arising from multiplication of quantum integers. Zbl 1066.39020
Nathanson, Melvyn B.
2004
Generalized additive bases, König’s lemma, and the Erdős–Turán conjecture. Zbl 1090.11010
Nathanson, Melvyn B.
2004
Representation functions of additive bases for abelian semigroups. Zbl 1122.11006
Nathanson, Melvyn B.
2004
The inverse problem for representation functions of additive bases. Zbl 1130.11009
Nathanson, Melvyn B.
2004
Unique representation bases for the integers. Zbl 1154.11306
Nathanson, Melvyn B.
2003
A functional equation arising from multiplication of quantum integers. Zbl 1055.39039
Nathanson, Melvyn B.
2003
Polynomial growth of sumsets in abelian semigroups. Zbl 1077.11014
Nathanson, Melvyn B.; Ruzsa, Imre Z.
2002
On Erdős’s elementary method in the asymptotic theory of partitions. Zbl 1112.11049
Nathanson, M. B.
2002
Elementary methods in number theory. Zbl 0953.11002
Nathanson, Melvyn B.
2000
Convexity and sumsets. Zbl 0998.11010
Elekes, György; Nathanson, Melvyn B.; Ruzsa, Imre Z.
2000
Growth of sumsets in Abelian semigroups. Zbl 0959.20055
Nathanson, Melvyn B.
2000
Partitions with parts in a finite set. Zbl 0969.11035
Nathanson, Melvyn B.
2000
Asymptotic density and the asymptotics of partition functions. Zbl 0999.11062
Nathanson, M. B.
2000
Number theory and semigroups of intermediate growth. Zbl 0990.20037
Nathanson, Melvyn B.
1999
Inverse theorems and the number of sums and products. Zbl 0947.11008
Nathanson, Melvyn B.; Tenenbaum, Gérald
1999
Linear forms in finite sets of integers. Zbl 0911.11008
Han, Shu-Ping; Kirfel, Christoph; Nathanson, Melvyn B.
1998
On sums and products of integers. Zbl 0869.11010
Nathanson, Melvyn B.
1997
Ballot numbers, alternating products, and the Erdös-Heilbronn conjecture. Zbl 0871.05003
Nathanson, Melvyn B.
1997
Additive number theory. Inverse problems and the geometry of sumsets. Zbl 0859.11003
Nathanson, Melvyn B.
1996
Additive number theory. The classical bases. Zbl 0859.11002
Nathanson, Melvyn B.
1996
The polynomial method and restricted sums of congruence classes. Zbl 0861.11006
Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre
1996
Adding distinct congruence classes modulo a prime. Zbl 0849.11081
Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre
1995
Inverse theorems for subset sums. Zbl 0835.11006
Nathanson, Melvyn B.
1995
Independence of solution sets and minimal asymptotic bases. Zbl 0828.11006
Erdős, Paul; Nathanson, Melvyn B.; Tetali, Prasad
1995
An inverse theorem for sums of sets of lattice points. Zbl 0802.11008
Nathanson, Melvyn B.
1994
The simplest inverse problems in additive number theory. Zbl 0804.11008
Nathanson, Melvyn B.
1993
On a problem of Rohrbach for finite groups. Zbl 0760.11003
Nathanson, Melvyn B.
1992
Simultaneous systems of representatives and combinatorial number theory. Zbl 0689.10062
Nathanson, Melvyn B.
1990
A simple construction of minimal asymptotic bases. Zbl 0683.10043
Jia, Xingde; Nathanson, Melvyn B.
1989
Sumsets containing long arithmetic progressions and powers of 2. Zbl 0693.10040
Nathanson, Melvyn B.; Sárközy, András
1989
Additive problems in combinatorial number theory. Zbl 0694.10049
Nathanson, Melvyn B.
1989
Additive bases with many representations. Zbl 0692.10045
Erdős, Paul; Nathanson, Melvyn B.
1989
On the maximum density of minimal asymptotic bases. Zbl 0674.10041
Nathanson, Melvyn B.; Sárközy, András
1989
Number theory. A seminar held at the Graduate School and University Center of the City University of New York 1985-88. Zbl 0674.00007
Chudnovsky, David V. (ed.); Chudnovsky, Gregory V. (ed.); Cohn, Harvey (ed.); Nathanson, Melvyn B. (ed.)
1989
Minimal bases and powers of 2. Zbl 0601.10040
Nathanson, Melvyn B.
1988
Minimal asymptotic bases with prescribed densities. Zbl 0651.10035
Erdős, Paul; Nathanson, Melvyn B.
1988
Sumsets containing infinite arithmetic progressions. Zbl 0633.10047
Erdős, Paul; Nathanson, Melvyn B.; Sárközy, András
1988
Simultaneous systems of representatives for families of finite sets. Zbl 0709.05006
Nathanson, Melvyn B.
1988
Multiplicative representations of integers. Zbl 0621.10040
Nathanson, Melvyn B.
1987
A short proof of Cauchy’s polygonal number theorem. Zbl 0611.10036
Nathanson, Melvyn B.
1987
Problems and results on minimal bases in additive number theory. Zbl 0622.10041
Erdős, Paul; Nathanson, Melvyn B.
1987
An extremal problem for least common multiples. Zbl 0619.10054
Nathanson, Melvyn B.
1987
Cofinite subsets of asymptotic bases for the positive integers. Zbl 0578.10056
Nash, John C. M.; Nathanson, Melvyn B.
1985
The exact order of subsets of additive bases. Zbl 0544.10058
Nathanson, Melvyn B.
1984
Number theory. A seminar held at the Graduate School and University Center of the City University of New York 1982. Zbl 0523.00002
Chudnovsky, D. V. (ed.); Chudnovsky, G. V. (ed.); Cohn, Harvey (ed.); Nathanson, M. B. (ed.)
1984
Largest and smallest maximal sets of pairwise disjoint partitions. Zbl 0512.10008
Nathanson, Melvyn B.
1983
Lagrange’s theorem and thin subsequences of squares. Zbl 0539.10038
Erdős, Paul; Nathanson, Melvyn B.
1981
Waring’s problem for sets of density zero. Zbl 0476.10042
Nathanson, Melvyn B.
1981
Sumsets contained in infinite sets of integers. Zbl 0451.10036
Nathanson, Melvyn B.
1980
Arithmetic progressions contained in sequences with bounded gaps. Zbl 0444.10053
Nathanson, Melvyn B.
1980
Classification problems in K-categories. Zbl 0457.18007
Nathanson, Melvyn B.
1980
Lagrange’s theorem with $$N^{1/3}$$ squares. Zbl 0436.10024
Choi, S. L. G.; Erdős, Paul; Nathanson, Melvyn B.
1980
...and 30 more Documents
all top 5

#### Cited by 662 Authors

 46 Nathanson, Melvyn Bernard 23 Chen, Yonggao 18 Sun, Zhi-Wei 16 Grynkiewicz, David J. 13 Tang, Min 11 Gao, Weidong 11 Miller, Steven J. 10 Chang, Mei-Chu 10 Hamidoune, Yahya Ould 10 Jin, Renling 10 Plagne, Alain 7 Bourgain, Jean 7 Jia, Xingde 7 Naduvath, Sudev 7 Ruzsa, Imre Z. 7 Sándor, Csaba 7 Serra, Oriol 6 Chu, Hùng Việt 6 Fang, Jinhui 6 Károlyi, Gyula 6 Longobardi, Patrizia 6 Maj, Mercede 6 Pan, Hao 6 Shkredov, Il’ya Dmitrievich 6 Yang, Quanhui 5 Adhikari, Sukumar Das 5 Freiman, Gregory A. 5 Garaev, Moubariz Z. 5 Germina, K. A. 5 Grekos, Georges 5 Kiss, Sándor Z. 5 Lev, Vsevolod F. 4 Alon, Noga M. 4 Bhanja, Jagannath 4 Caldeira, Cristina 4 Chen, Fengjuan 4 Chithra, Kaithavalappil 4 Cilleruelo, Javier 4 Eliahou, Shalom 4 Erdős, Pál 4 Han, Dongchun 4 Hegyvári, Norbert 4 Herzog, Marcel 4 Konyagin, Sergeĭ Vladimirovich 4 Larsen, Michael Jeffrey 4 Lecouvey, Cédric 4 Ling, Dengrong 4 McNew, Nathan 4 Mirek, Mariusz 4 Nguyen, Lan T. T. 4 Ordaz, Oscar 4 Pandey, Ram Krishna 4 Perdigão Dias da Silva, José António 4 Qu, Yongke 4 Schoen, Tomasz 4 Shalev, Aner 4 Stanchescu, Yonutz V. 4 Tao, Terence 4 Thangadurai, Ravindranathan 4 Witte Morris, Dave 4 Zémor, Gilles 3 Balandraud, Éric 3 Green, Ben Joseph 3 Han, Sandie 3 Hegarty, Peter V. 3 Helou, Charles 3 Hong, Shaofang 3 Hou, Xiang-Dong 3 Kervaire, Michel A. 3 Li, Yali 3 Masuda, Ariane M. 3 Mistri, Raj Kumar 3 Nguyen, Lan 3 Petrov, Fedor Vladimirovich 3 Puš, Vladimír 3 Rozgonyi, Eszter 3 Rudnev, Misha 3 Schmid, Wolfgang Alexander 3 Singh, Satyanand 3 Solymosi, József 3 Sun, Cuifang 3 Thiel, Johann A. 3 Tringali, Salvatore 3 Vu, Van H. 3 Zhang, Hanbin 3 Zhao, Yufei 2 Akhtar, Reza 2 Asada, Megumi 2 Bajnok, Béla 2 Banks, William D. 2 Bezuglyi, Sergey I. 2 Biswas, Arindam 2 Borisov, Alexander 2 Borwein, Peter Benjamin 2 Christopher, A. David 2 Croot, Ernie 2 Deshouillers, Jean-Marc 2 Du, Bau-Sen 2 Dubickas, Artūras 2 Elekes, György ...and 562 more Authors
all top 5

#### Cited in 150 Serials

 97 Journal of Number Theory 33 Discrete Mathematics 27 Proceedings of the American Mathematical Society 24 Journal of Combinatorial Theory. Series A 24 International Journal of Number Theory 22 European Journal of Combinatorics 20 Bulletin of the Australian Mathematical Society 18 Israel Journal of Mathematics 15 Integers 12 Transactions of the American Mathematical Society 12 Journal de Théorie des Nombres de Bordeaux 11 Advances in Mathematics 11 Combinatorica 10 The Ramanujan Journal 9 Linear Algebra and its Applications 7 Acta Arithmetica 7 Archiv der Mathematik 7 Functiones et Approximatio. Commentarii Mathematici 7 Journal of Algebra 7 Acta Mathematica Hungarica 7 SIAM Journal on Discrete Mathematics 7 Finite Fields and their Applications 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 American Mathematical Monthly 5 Communications in Algebra 5 Journal d’Analyse Mathématique 5 Periodica Mathematica Hungarica 5 Duke Mathematical Journal 5 Advances in Applied Mathematics 5 Combinatorics, Probability and Computing 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Journal of Algebra and its Applications 4 Journal of Mathematical Analysis and Applications 4 Mathematical Notes 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Mathematics of Computation 4 Annales de l’Institut Fourier 4 Journal of Combinatorial Theory. Series B 4 Journal of Pure and Applied Algebra 4 Theoretical Computer Science 4 Discrete & Computational Geometry 4 Journal of the American Mathematical Society 4 Aequationes Mathematicae 4 Indagationes Mathematicae. New Series 4 Annals of Mathematics. Second Series 3 Discrete Applied Mathematics 3 Applied Mathematics and Computation 3 Czechoslovak Mathematical Journal 3 Journal of Functional Analysis 3 Mathematische Zeitschrift 3 Rendiconti del Seminario Matematico della Università di Padova 3 Bulletin of the American Mathematical Society. New Series 3 Journal of the Australian Mathematical Society 3 Discrete Mathematics, Algorithms and Applications 3 Science China. Mathematics 2 Rocky Mountain Journal of Mathematics 2 The Mathematical Intelligencer 2 Beiträge zur Algebra und Geometrie 2 Inventiones Mathematicae 2 Mathematica Slovaca 2 Mathematika 2 Semigroup Forum 2 Random Structures & Algorithms 2 Expositiones Mathematicae 2 Journal of Mathematical Sciences (New York) 2 Journal of Integer Sequences 2 Journal of the European Mathematical Society (JEMS) 2 Proceedings of the Steklov Institute of Mathematics 2 Asian-European Journal of Mathematics 2 International Journal of Combinatorics 2 International Journal of Group Theory 1 International Journal of Modern Physics B 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Advances in Applied Probability 1 Information Processing Letters 1 Journal of Mathematical Physics 1 Lithuanian Mathematical Journal 1 The Mathematical Gazette 1 Ukrainian Mathematical Journal 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Calcolo 1 Collectanea Mathematica 1 Functional Analysis and its Applications 1 Information Sciences 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematical Economics 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Journal of Statistical Planning and Inference 1 The Journal of Symbolic Logic 1 Mathematische Annalen 1 Monatshefte für Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Topology and its Applications 1 Moscow University Computational Mathematics and Cybernetics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Bulletin of the Korean Mathematical Society 1 SIAM Journal on Algebraic and Discrete Methods ...and 50 more Serials
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#### Cited in 42 Fields

 514 Number theory (11-XX) 145 Combinatorics (05-XX) 107 Group theory and generalizations (20-XX) 21 Convex and discrete geometry (52-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 15 Mathematical logic and foundations (03-XX) 15 Field theory and polynomials (12-XX) 14 Dynamical systems and ergodic theory (37-XX) 14 Computer science (68-XX) 13 Associative rings and algebras (16-XX) 11 Difference and functional equations (39-XX) 10 Measure and integration (28-XX) 10 Information and communication theory, circuits (94-XX) 8 Algebraic geometry (14-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Geometry (51-XX) 7 Commutative algebra (13-XX) 7 Real functions (26-XX) 7 Probability theory and stochastic processes (60-XX) 5 General topology (54-XX) 5 Numerical analysis (65-XX) 5 Quantum theory (81-XX) 4 Special functions (33-XX) 4 Functional analysis (46-XX) 3 Functions of a complex variable (30-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Ordinary differential equations (34-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Category theory; homological algebra (18-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX)

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