Problems in Analytic Number Theory

By: M. Ram Murty

Write A Review

Hardcover | 10 March 2008 | Edition Number 2

At a Glance

Hardcover
528 Pages

Edition Type
Revised

Dimensions(cm)
23.6 x 16.0 x 2.9

Hardcover

$89.99

or 4 interest-free payments of $22.50 with

or

Ships in 5 to 7 business days

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, Frankfurt am Main

Industry 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: "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)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Number Theory

Elements of Number Theory - Emanuel Patterson

$271.99

14%
OFF

Iwasawa Theory and Its Perspective, Volume 3

Paperback

RRP $312.00

$306.99

Iwasawa Theory and Its Perspective (Volumes 1-3) - Tadashi Ochai

$187.75

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Paperback

RRP $56.99

$56.75

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Hardcover

RRP $399.00

$341.75

14%
OFF

Primes in Arithmetic Progressions to Large Moduli I

Fixed Residue Classes

Paperback

RRP $197.00

$187.75

Primes in Arithmetic Progressions to Large Moduli III : Uniform Residue Classes - James Maynard

$174.99

Differential Modules over Differential Rings : Chapman & Hall/CRC Monographs and Research Notes in Mathematics - Andy R. Magid

$233.75

Introduction to Modern Cryptography : Revised Third Edition - Jonathan Katz

$290.99

Multivariable Calculus Set Free : Infinitesimals Ride Again - ?? ???, C. Bryan Dawson

$52.75

Elementary Number Theory

Hardcover

$433.75

Preface to the Second Edition	p. vii
Acknowledgments for the Second Edition	p. ix
Preface to the First Edition	p. xi
Acknowledgments for the First Edition	p. xv
Problems	p. 1
Arithmetic Functions	p. 3
The M&duml;bius Inversion Formula and Applications	p. 4
Formal Dirichlet Series	p. 7
Orders of Some Arithmetical Functions	p. 9
Average Orders of Arithmetical Functions	p. 10
Supplementary Problems	p. 11
Primes in Arithmetic Progressions	p. 17
Summation Techniques	p. 17
Characters mod q	p. 22
Dirichlet's Theorem	p. 24
Dirichlet's Hyperbola Method	p. 27
Supplementary Problems	p. 29
The Prime Number Theorem	p. 35
Chebyshev's Theorem	p. 36
Nonvanishing of Dirichlet Series on Re(s)=1	p. 39
The Ikehara - Wiener Theorem	p. 42
Supplementary Problems	p. 48
The Method of Contour Integration	p. 53
Some Basic Integrals	p. 53
The Prime Number Theorem	p. 57
Further Examples	p. 62
Supplementary Problems	p. 65
Functional Equations	p. 69
Poisson's Summation Formula	p. 69
The Riemann Zeta Function	p. 72
Gauss Sums	p. 75
Dirichlet L-functions	p. 76
Supplementary Problems	p. 79
Hadamard Products	p. 85
Jensen's Theorem	p. 85
Entire Functions of Order 1	p. 88
The Gamma Function	p. 91
Infinite Products for (s) and (s,x)	p. 93
Zero-Free Regions for (s) and L(s,x)	p. 94
Supplementary Problems	p. 99
Explicit Formulas	p. 101
Counting Zeros	p. 101
Explicit Formula for (x)	p. 104
Weil's Explicit Formula	p. 107
Supplementary Problems	p. 110
The Selberg Class	p. 115
The Phragmén - Lindeloüf Theorem	p. 116
Basic Properties	p. 118
Selberg's Conjectures	p. 123
Supplementary Problems	p. 125
Sieve Methods	p. 127
The Sieve of Eratosthenes	p. 127
Brun's Elementary Sieve	p. 133
Selberg's Sieve	p. 138
Supplementary Problems	p. 144
p-adic Methods	p. 147
Ostrowski's Theorem	p. 147
Hensel's Lemma	p. 155
p-adic Interpolation	p. 159
The p-adic Zeta-Function	p. 165
Supplementary Problems	p. 168
Equidistribution	p. 171
Uniform distribution modulo 1	p. 171
Normal numbers	p. 177
Asymptotic distribution functions mod 1	p. 180
Discrepancy	p. 182
Equidistribution and L-functions	p. 189
Supplementary Problems	p. 193
Solutions	p. 197
Arithmetic Functions	p. 199
The Möbius Inversion Formula and Applications	p. 199
Formal Dirichlet Series	p. 208
Orders of Some Arithmetical Functions	p. 212
Average Orders of Arithmetical Functions	p. 215
Supplementary Problems	p. 220
Primes in Arithmetic Progressions	p. 237
Characters mod q	p. 237
Dirichlet's Theorem	p. 246
Dirichlet's Hyperbola Method	p. 251
Supplementary Problems	p. 257
The Prime Number Theorem	p. 273
Chebyshev's Theorem	p. 273
Nonvanishing of Dirichlet Series on Re(s)=1	p. 280
The Ikehara - Wiener Theorem	p. 288
Supplementary Problems	p. 292
The Method of Contour Integration	p. 305
Some Basic Integrals	p. 305
The Prime Number Theorem	p. 311
Further Examples	p. 314
Supplementary Problems	p. 317
Functional Equations	p. 329
Poisson's Summation Formula	p. 329
The Riemann Zeta Function	p. 332
Gauss Sums	p. 333
Dirichlet L-functions	p. 335
Supplementary Problems	p. 338
Hadamard Products	p. 357
Jensen's Theorem	p. 357
The Gamma Function	p. 358
Infinite Products for (s) and (s,x)	p. 369
Zero-Free Regions for (s) and L(s,x)	p. 374
Supplementary Problems	p. 379
Explicit Formulas	p. 385
Counting Zeros	p. 385
Explicit Formula for (x)	p. 388
Supplementary Problems	p. 393
The Selberg Class	p. 403
The Phragmén - Lindeloüf Theorem	p. 403
Basic Properties	p. 404
Selberg's Conjectures	p. 411
Supplementary Problems	p. 417
Sieve Methods	p. 423
The Sieve of Eratosthenes	p. 423
Brun's Elementary Sieve	p. 429
Selberg's Sieve	p. 432
Supplementary Problems	p. 439
p-adic Methods	p. 449
Ostrowski's Theorem	p. 449
Hensel's Lemma	p. 454
p-adic Interpolation	p. 456
The p-adic -Function	p. 463
Supplementary Problems	p. 468
Equidistribution	p. 475
Uniform distribution modulo 1	p. 475
Normal numbers	p. 483
Asymptotic distribution functions mod 1	p. 484
Discrepancy	p. 485
Equidistribution and L-functions	p. 488
Supplementary Problems	p. 490
References	p. 497
Index	p. 499
Table of Contents provided by Ingram. All Rights Reserved.

Problems in Analytic Number Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Number Theory

Elements of Number Theory

Monomial Algebras

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Iwasawa Theory and Its Perspective, Volume 3

Iwasawa Theory and Its Perspective (Volumes 1-3)

Experimental Mathematics

A Computational Perspective

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Primes in Arithmetic Progressions to Large Moduli I

Fixed Residue Classes

Primes in Arithmetic Progressions to Large Moduli III

Uniform Residue Classes

Primes in Arithmetic Progressions to Large Moduli II

Well-Factorable Estimates

Ergodic Theory

Differential Modules over Differential Rings

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Introduction to Modern Cryptography

Chapman & Hall/Crc Cryptography and Network Security

Introduction to Modern Cryptography

Revised Third Edition

Srinivasa Ramanujan

His Life, Legacy, and Mathematical Influence

Nankai Symposium on Mathematical Dialogues

Celebrating the 110th Anniversary of the birth of Prof. S.-S. Chern

Algebraic Structures and Applications

Multivariable Calculus Set Free

Infinitesimals Ride Again

Adelic Line Bundles on Quasi-projective Varieties

Annals of Mathematics Studies

Reading, Writing, and Proving

A Closer Look at Mathematics

Multiplicative Number Theory II

Primes and Sieves

From Classical L-Functions to Modern Reciprocity Laws

Graduate Texts in Mathematics

Mathematical Puzzles

Revised Edition

Elementary Number Theory

This product is categorised by