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Introduction to Analytic and Probabilistic Number Theory: Third Edition

About this Title

Gérald Tenenbaum, Institut Élie Cartan, Vandoeuvre-lès Nancy, France. Translated by Dr Patrick D F Ion

Publication: Graduate Studies in Mathematics
Publication Year: 2015; Volume 163
ISBNs: 978-0-8218-9854-3 (print); 978-1-4704-2223-3 (online)
DOI: https://doi.org/10.1090/gsm/163
MathSciNet review: MR3363366
MSC: Primary 11-02; Secondary 11Kxx, 11Mxx, 11Nxx

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Table of Contents

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Front/Back Matter

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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