Overview

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.

Full Product Details

Author:   Melvyn B. Nathanson
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 1996
Volume:   164
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.551kg
ISBN:  

9781441928481

ISBN 10:   1441928480
Pages:   342
Publication Date:   19 November 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I Waring’s problem.- 1 Sums of polygons.- 2 Waring’s problem for cubes.- 3 The Hilbert—Waring theorem.- 4 Weyl’s inequality.- 5 The Hardy—Littlewood asymptotic formula.- II The Goldbach conjecture.- 6 Elementary estimates for primes.- 7 The Shnirel’man—Goldbach theorem.- 8 Sums of three primes.- 9 The linear sieve.- 10 Chen’s theorem.- III Appendix.- Arithmetic functions.- A.1 The ring of arithmetic functions.- A.2 Sums and integrals.- A.3 Multiplicative functions.- A.4 The divisor function.- A.6 The Möbius function.- A.7 Ramanujan sums.- A.8 Infinite products.- A.9 Notes.- A.10 Exercises.

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)

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)

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