Additive Number Theory The Classical Bases: 164 (Graduate Texts in Mathematics, 164) - Hardcover

Nathanson, Melvyn B.

Hardcover

ISBN 10: 038794656X ISBN 13: 9780387946566

Publisher: Springer, 1996

Synopsis

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] 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 used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

About this title

Product Description

Describes the problems in additive number theory, and introduces the circle method and the sieve method, which are the basic analytical and combinatorial tools to attack these problems. Intended for students who want to learn additive number theory, the prerequisites for this book are undergraduate courses in number theory and real analysis.

Review

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)

Edition details

• Publisher: Springer
• Publication date: 1996
• ISBN 10: 038794656X
• ISBN 13: 9780387946566
• Binding: Hardcover
• Language: English
• Number of pages: 356