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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
List of contents
Problems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.
Summary
This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It provides a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers.
Additional text
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)
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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)
