Overview
- Contains a combination of well-organized theory and problems
- The problems successfully guide students through the most important areas of analytic number theory
- Includes more than 500 exercises at varying levels of difficulty
- Covers an improved Eratosthenes sieve, without the typical combinatorics
- Includes a clear exposition of Brun’s and Selberg’s sieves
- Includes supplementary material: sn.pub/extras
Part of the book series: Graduate Texts in Mathematics (GTM, volume 206)
Part of the book sub series: Readings in Mathematics (READMATH)
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Table of contents (22 chapters)
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Front Matter
Keywords
About this book
This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory. The new edition has been completely rewritten, errors have been corrected, and there is a new chapter on equidistribution.
About the first edition:
"...this monograph gives important results and techniques for specific topics, together with many exercises; it is not possible to describe adequately the wealth of material covered in this book."
- Wolfgang Schwarz, Zentralblatt
Reviews
M.R. Murty
Problems in Analytic Number Theory
"The reviewer strongly approves of the problem-based approach to learning, and recommends this book to any student of analytic number theory."
—MATHEMATICAL REVIEWS
From the reviews of the second edition:
“This expanded and corrected second edition of this useful and interesting book has a new chapter on the topic of equidistribution. … this monograph gives important results and techniques for specific topics, together with many exercises. … I do enjoy this book … and I imagine when I take the graduate course in the subject that it will be of a greater benefit, which is why I offered such a high rating.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)
"The second edition of the book has eleven chapters … . the book can be used both as a problem book (as its title shows) and also as a textbook (as the series in which the book is published shows). … is ideal as a text for a first course in analytic number theory, either at the senior undergraduate or the graduate level. … I believe that this book will be very useful for students, researchers and professors. It is well written … ." (Mehdi Hassani, MathDL, April, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Problems in Analytic Number Theory
Authors: M. Ram Murty
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-72350-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-72349-5Published: 18 December 2007
Softcover ISBN: 978-1-4419-2477-3Published: 19 November 2010
eBook ISBN: 978-0-387-72350-1Published: 16 April 2008
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XXII, 506
Topics: Number Theory, Combinatorics