Overview

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.

Full Product Details

Author:   Gerald Tenenbaum
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   3rd Revised edition
Volume:   163
ISBN:  

9781470478216

ISBN 10:   1470478218
Pages:   629
Publication Date:   31 January 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

Part I. Elementary methods Chapter I.0. Some tools from real analysis Chapter I.1. Prime numbers Chapter I.2. Arithmetic functions Chapter I.3. Average orders Chapter I.4. Sieve methods Chapter I.5. Extremal orders Chapter I.6. The method of van der Corput Chapter I.7. Diophantine approximation Part II. Complex analysis methods Chapter II.0. The Euler gamma function Chapter II.1. Generating functions: Dirichlet series Chapter II.2. Summation formulae Chapter II.3. The Riemann zeta function Chapter II.4. The prime number theorem and the Riemann hypothesis Chapter II.5. The Selberg-Delange method Chapter II.6. Two arithmetic applications Chapter II.7. Tauberian theorems Chapter II.8. Primes in arithmetic progressions Part III. Probabilistic methods Chapter III.1. Densities Chapter III.2. Limiting distributions of arithmetic functions Chapter III.3. Normal order Chapter III.4. Distribution of additive functions and mean values of multiplicative functions Chapter III.5. Friable integers. The saddle-point method Chapter III.6. Integers free of small factors

Reviews

“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

Author Information

Gerald Tenenbaum, Institut Elie Cartan, Vandoeuvre-les Nancy, France.

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