Analytic Number Theory

Donald J. Newman (auth.)0387983082, 9780387983080, 9780387227405

Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author’s heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdös-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A “Natural” Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem – all presented in a surprisingly elegant and efficient manner with clever examples and interesting problems in each chapter. This text is suitable for a graduate course in analytic number theory.

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Table of contents :
The Idea of Analytic Number Theory….Pages 1-15
The Partition Function….Pages 17-30
The Erdős-Fuchs Theorem….Pages 31-39
Sequences without Arithmetic Progressions….Pages 41-48
The Waring Problem….Pages 49-57
A “Natural” Proof of the Nonvanishing of L -Series….Pages 59-65
Simple Analytic Proof of the Prime Number Theorem….Pages 67-75