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.

Review

From the reviews:

D. J. Newman

Analytic Number Theory

“This book is remarkable . . . The author’s style remains pleasantly discursive throughout the book. Any of these chapters might be useful to a reader planning a lecture course in the relevant subject area . . . The student of analytic number theory would do well to find shelf-room for this book.”―MATHEMATICAL

“Donald J. Newman was a noted problem-solver who believed that math should be fun and that beautiful theorems should have beautiful proofs. This short book collects brief, self-contained proofs of several well-known theorems in analytic number theory … .” (Allen Stenger, The Mathematical Association of America, November, 2010)

Table of Contents

I. The Idea of Analytic Number Theory

II. The Partition Function

III. The Erdos–Fuchs Theorem

IV. Sequences without Arithmetic Progressions

V. The Waring Problem

VI. A “Natural” Proof of the Nonvanishing of L-Series

VII. Simple Analytic Proof of the Prime Number Theorem