Additive Number Theory The Classical Bases

Hardcover | June 25, 1996

byMelvyn B. Nathanson

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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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From Our Editors

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...

From the Publisher

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...

From the Jacket

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...

Format:HardcoverDimensions:358 pages, 9.21 × 6.14 × 0.27 inPublished:June 25, 1996Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:038794656X

ISBN - 13:9780387946566

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Table of Contents

Contents: Sums of Polygons.- Waring's Problem for Cubes.- The Hilbert-Waring Theorem.- Weyl's Inequality.- The Hardy-Littlewood Asymptotic Formula.- Elementary Estimates for Primes.- The Shnirel'man-Goldbach Theorem.- Sums of Three Primes.- The Linear Sieve.- Chen's Theorem A Arithmetic Functions.

From Our Editors

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. Additive number theory is one of the oldest and richest areas of mathematics. This book is the first comprehensive treatment of the su

Editorial Reviews

From the reviews:"This book provides a very thorough exposition of work to date on two classical problems in additive number theory . . is aimed at students who have some background in number theory and a strong background in real analysis. A novel feature of the book, and one that makes it very easy to read, is that all the calculations are written out in full - there are no steps 'left to the reader'. . The book also includes a large number of exercises . ." (Allen Stenger, The Mathematical Association of America, August, 2010)