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- Description[Hilbert's] style has t 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 t. H. Weyl  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, t for experts who already kw 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 nnegative integer is the sum of four squares. In general, the set A of nnegative integers is called an additive basis of order h if every nnegative integer can be written as the sum of h t 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.
- Author(s)Melvyn B. Nathanson
- PublisherSpringer-Verlag New York Inc.
- Date of Publication19/10/2010
- Series TitleGraduate Texts in Mathematics
- Series Part/Volume Number164
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight505 g
- Width156 mm
- Height234 mm
- Spine18 mm
- Format DetailsTrade paperback (US)
- Edition Statement1st ed. Softcover of orig. ed. 1996
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