- Contains a large selection of problems with fully worked-out solutions
- Covers an improved Eratosthenes sieve, without the typical combinatorics
- Focuses on the distribution of prime numbers
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- About this Textbook
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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
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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)
- Table of contents (22 chapters)
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Arithmetic Functions
Pages 3-15
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Primes in Arithmetic Progressions
Pages 17-33
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The Prime Number Theorem
Pages 35-51
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The Method of Contour Integration
Pages 53-68
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Functional Equations
Pages 69-83
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Table of contents (22 chapters)
- Download Preface 1 PDF (34.9 KB)
- Download Sample pages 1 PDF (346.7 KB)
- Download Table of contents PDF (134.2 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Problems in Analytic Number Theory
- Authors
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- M. Ram Murty
- Series Title
- Readings in Mathematics
- Series Volume
- 206
- Copyright
- 2008
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag New York
- eBook ISBN
- 978-0-387-72350-1
- DOI
- 10.1007/978-0-387-72350-1
- Hardcover ISBN
- 978-0-387-72349-5
- Softcover ISBN
- 978-1-4419-2477-3
- Edition Number
- 2
- Number of Pages
- XXII, 506
- Topics
