**Graduate Studies in Mathematics**

Volume: 163;
2015;
629 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-0-8218-9854-3

Product Code: GSM/163

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-2223-3
Product Code: GSM/163.E**

List Price: $89.00

Individual Member Price: $71.20

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#### Supplemental Materials

# Introduction to Analytic and Probabilistic Number Theory: Third Edition

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*Gérald Tenenbaum*

This book provides a self contained, thorough introduction to the
analytic and probabilistic methods of number theory. The prerequisites
being reduced to classical contents of undergraduate courses, it
offers to students and young researchers a systematic and consistent
account on the subject. It is also a convenient tool for professional
mathematicians, who may use it for basic references concerning many
fundamental topics.

Deliberately placing the methods before the results, the book will
be of use beyond the particular material addressed directly. Each
chapter is complemented with bibliographic notes, useful for
descriptions of alternative viewpoints, and detailed exercises, often
leading to research problems.

This third edition of a text that has become classical offers a
renewed and considerably enhanced content, being expanded by more than
50 percent. Important new developments are included, along with
original points of view on many essential branches of arithmetic and
an accurate perspective on up-to-date bibliography.

The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate.

—Mathematical Reviews

#### Table of Contents

# Table of Contents

## Introduction to Analytic and Probabilistic Number Theory: Third Edition

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Foreword xv16
- Preface to the third edition xix20
- Preface to the English translation xxi22
- Notation xxiii24
- Part I. Elementary methods 126
- Chapter I.0: Some tools from real analysis 328
- Chapter I.1: Prime numbers 1136
- Chapter I.2: Arithmetic functions 2954
- Chapter I.3: Average orders 4368
- Chapter I.4: Sieve methods 6792
- Chapter I.5: Extremal orders 111136
- Chapter I.6: The method of van der Corput 123148
- Chapter I.7: Diophantine approximation 145170
- Part II. Complex analysis methods 167192
- Chapter II.0: The Euler gamma function 169194
- Chapter II.1: Generating functions: Dirichlet series 187212
- Chapter II.2: Summation formulae 217242
- Chapter II.3: The Riemann zeta function 231256
- Chapter II.4: The prime number theorem and the Riemann hypothesis 261286
- Chapter II.5: The Selberg-Delange method 277302
- Chapter II.6: Two arithmetic applications 299324
- Chapter II.7: Tauberian theorems 317342
- Chapter II.8: Primes in arithmetic progressions 359384
- Part III. Probabilistic methods 411436
- Chapter III.1: Densities 413438
- Chapter III.2: Limiting distributions of arithmetic functions 425450
- Chapter III.3: Normal order 445470
- Chapter III.4: Distribution of additive functions and mean values of multiplicative functions 475500
- Chapter III.5: Friable integers. The saddle-point method 511536
- Chapter III.6: Integers free of small factors 557582
- Bibliography 591616
- Index 617642
- Back Cover Back Cover1656

#### Readership

Graduate students and research mathematicians interested in number theory, analysis, and probability.