Additive Number Theory The Classical Bases | 
 enlarge | Author: Melvyn B. Nathanson
Publisher: Springer
Category: EBooks
List Price: $69.95
Buy New: $54.13
You Save: $15.82 (23%)
Rating:  2 reviews
Sales Rank: 84903
Format: Kindle Book
Media: Kindle Edition
Edition: 1
Pages: 364
Number Of Items: 1
Dewey Decimal Number: 512.72
Publication Date: June 25, 1996
Availability: Usually ships in 24 hours
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Product Description
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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| Customer Reviews:
Clear coverage of Waring's Problem and Goldbach Conjecture April 22, 2002
13 out of 14 found this review helpful
This book gives clear and complete proofs of Waring's Problem (that every positive integer is the sum of a bounded number of nth powers) and of all current results in the Goldbach Conjecture (Brun's theorem that the sum of the reciprocals of the twin primes converges, Vinogradov's theorem that every large odd integer is the sum of three primes, and Chen's theorem that every large even integer is the sum of a prime and and number that is either prime or the product of two primes). The focus of the book is these specific problems; it develops many general methods while attacking these problems, but does not develop the general methods for their own sake. The book assumes a little prior knowledge of analysis and number theory, and it quotes a few advanced results (for example, the Bombieri-Vinogradov theorem on primes in arithmetic progressions) that are proved in Davenport's book "Multiplicative Number Theory", but otherwise it is a complete exposition of these two problems.The best feature of the book, apart from its complete coverage, is that all the calculations are written out in full; there's no need to keep your pencil and paper handy to check the steps. This is especially valuable in the sieve sections where the combinatorial explosion can be overwhelming. The exercises are the weak point of the book; most of them are either routine or are omitted steps from proofs, and they don't present much challenge to someone who has already worked through the body of the book. The book's layout and production quality are good. There are only a small number of typographical errors, none confusing.
Advanced graduate level text in additive number theory October 21, 2007
Stuart-Little
3 out of 3 found this review helpful
Advanced graduate level text in additive number theory, covers the classical bases. This book is the first comprehensive treatment of the subject in 40 years. If the topic of additive number theory interests you, then this is the book to get as there is no comparable (single) book available. Requires a solid understanding of complex analysis. Note, a nice introduction to additive number theory can be found in Hardy and Wright's Introduction to Number Theory.
Some highlights: 1) 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. 2) Brun's sieve for upper bound on the number of twin primes. 3) Vinogradov's simplification of the Hardy, Littlewood, and Ramanujan's circle method.
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