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Additive Number Theory : Density Theorems and the Growth of Sumsets

This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. Nathanson's numerous results have been widely published in top notch journals and in a number of excellent graduate textbooks (GTM Springer) and reference works. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.

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  • "The classical bases in additive number theory are the polygonal numbers, the squares, cubes, and higher powers, and the primes. This book contains many of the great theorems in this subject: Cauchy's polygonal number theorem, Linnik's theorem on sums of cubes, Hilbert's proof of Waring's problem, the Hardy-Littlewood asymptotic formula for the number of representations of an integer as the sum of positive kth powers, Shnirel'man's theorem that every integer greater than one is the sum of a bounded number of primes, Vinogradov's theorem on sums of three primes, and Chen's theorem that every sufficiently large even integer is the sum of a prime and a number that is either prime or the product of two primes. The book is also an introduction to the circle method and sieve methods, which are the principal tools used to study the classical bases. The only prerequisites for the book are undergraduate courses in number theory and analysis."
  • "This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. Nathanson's numerous results have been widely published in top notch journals and in a number of excellent graduate textbooks (GTM Springer) and reference works. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research."@en
  • "Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse problem, one starts with a sumset hA and attempts to describe the structure of the underlying set A. In recent years, there has been remarkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression."
  • "The purpose of this book is to describe the classical problems in additive number theory, and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools to attack these problems. This book is intended for students who want to learn additive number theory, not for experts who already know it. The prerequisites for this book are undergraduate courses in number theory and real analysis."

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  • "Electronic books"
  • "Electronic books"@en
  • "Lehrbuch"
  • "Aufsatzsammlung"

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  • "Additive Number Theory : Density Theorems and the Growth of Sumsets"@en
  • "Additive number theory : festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson"
  • "Additive number theory : the classical bases"@en
  • "Additive number theory : the classical bases"
  • "Additive number theory Inverse problems and the geometry of sumsets"
  • "Additive number theory : The classical bases"
  • "Additive Number Theory Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson"
  • "Additive number theory The classical bases"
  • "Additive Number Theory The Classical Bases"
  • "Additive number theory : Festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson"
  • "Additive number theory : Inverse problems and the geometry of sumsets"
  • "Additive number theory : Festschrift in honor of the sixtieth birthday of Melvyn B. Nathason"
  • "Additive number theory festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson"
  • "Additive number theory festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson"@en
  • "Additive number theory"
  • "Additive Number Theory : Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson"
  • "Additive number theory : inverse problems and the geometry of sumsets"@en
  • "Additive number theory : inverse problems and the geometry of sumsets"
  • "The classical bases"
  • "Additive Number Theory the Classical Bases"

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