Analytic Number Theory

Graduate Texts in Mathematics #177

by Donald J. Newman

Some of the central topics in number theory, presnted in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace and emphasis on readability. His heartfelt enthusiasm enables readers to see what is magical about the subject. All the topics are presented in a refreshingly elegant and efficient manner with clever examples and interesting problems throughout. The text is suitable for a graduate course in analytic number theory.

Genres: Mathematics, Theory, Number

88 pages, Hardcover

First published December 19, 1997

Reviews

[Francisco Barrios]

According to the back cover, the book has an «emphasis on readability». As understood by its author, this might be a serious drawback though. The material covered is incredibly synthesized —I know, it's a graduate text, but that doesn't mean the proofs have to be painstakingly short or even obscure, just because the «topics are presented in a surprisingly elegant and efficient manner». Really? Even some references all along the text might have been helpful—, and most definitely this is NOT a book for beginners nor self study, unless you're willing to dedicate a big amount of time to grasp and understand page after page. 8 pages for a full response to the Waring Problem? Another 8 pages for two (!!) analytic proofs of the Prime Number Theorem?

All in all, each chapter provides an excellent source of material for many delightful seminars in applied complex analysis or analytic number theory, and could be used (if you're an advisor whose students have an inclination to analytic number theory) for writing many wonderful dissertations at the graduate level.