Analytic Number Theory

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.

The Idea of Analytic Number Theory. - The Partition Function. - The Erd? s-Fuchs Theorem. - Sequences without Arithmetic Progressions. - The Waring Problem. - A Natural Proof of the Nonvanishing of L-Series. - Simple Analytic Proof of the Prime Number Theorem.