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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
Table of Contents
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Front/Back Matter
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