Additive Number Theory The Classical Bases

AvMelvyn B. Nathanson

Häftad, Engelska, 2010

Del 164 i serien Graduate Texts in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2010-11-19
Mått:155 x 235 x 20 mm
Vikt:546 g
Format:Häftad
Språk:Engelska
Serie:Graduate Texts in Mathematics
Antal sidor:342
Förlag:Springer-Verlag New York Inc.
ISBN:9781441928481

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Recensioner i media

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)

Innehållsförteckning

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.