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Additive Number Theory The Classical Bases by Melvyn B. Nathanson (Paperback, 2010)

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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.

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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.