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Other titles in the Cambridge Studies in Advanced Mathematics series:
Cambridge Studies in Advanced Mathematics #46: Introduction to Analytic and Probabilistic Number Theoryby G. Tenenbaum
Synopses & Reviews
This book is a systematic introduction to analytic methods in number theory, and assumes as a prerequisite only what is taught in a standard undergraduate course. The author aids readers by including a section of bibliographic notes and detailed exercises at the end of each chapter. Tenenbaum has emphasized methods rather than results, so readers should be able to tackle more advanced material than is included here. Moreover, he covers developments on many new and unpublished topics, such as: the Selberg-Delange method; a version of the Ikehara-Ingham Tauberian theorem; and a detailed exposition of the arithmetical use of the saddle-point method.
This is a self-contained introduction to analytic methods in number theory.
Includes bibliographical references (p. -442) and index.
Table of Contents
Foreword; Notation; Part I. Elementary Methods: Some tools from real analysis; 1. Prime numbers; 2. Arithmetic functions; 3. Average orders; 4. Sieve methods; 5. Extremal orders; 6. The method of van der Corput; Part II. Methods of Complex Analysis: 1. Generating functions: Dirichlet series; 2. Summation formulae; 3. The Riemann zeta function; 4. The Prime Number Theorem and the Riemann Hypothesis; 5. The Selberg-Delange method; 6. Two arithmetic applications; 7. Tauberian theorems; 8. Prime numbers in arithmetic progressions; Part III. Probabilistic Methods: 1. Densities; 2. Limiting distribution of arithmetic functions; 3. Normal order; 4. Distribution of additive functions and mean values of multiplicative functions; 5. Integers free of large prime factors. The saddle-point method; 6. Integers free of small prime factors; Bibliography; Index.
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