A Course in Analytic Number Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 160) - Hardcover

Marius Overholt

Hardcover

ISBN 10: 1470417065 ISBN 13: 9781470417062

Publisher: American Mathematical Society, 2014

Synopsis

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

About this title

About the Author

Marius Overholt , University of Tromso, Norway.

Review

This book is a proper text for a graduate student (with a pretty strong background) keen on getting into analytic number theory, and it's quite a good one. It's well-written, rather exhaustive, and well-paced. The choice of themes is good, too, and will form a very sound platform for future studies and work in this gorgeous field. --MAA Reviews

Edition details

• Publisher: American Mathematical Society
• Publication date: 2014
• ISBN 10: 1470417065
• ISBN 13: 9781470417062
• Binding: Hardcover
• Language: English
• Number of pages: 371