Introduction to Analytic and Probabilistic Number Theory

Gerald Tenenbaum (Autor)

Buch | Softcover

629 Seiten

2015 | Third Edition
American Mathematical Society (Verlag)
978-1-4704-7821-6 (ISBN)

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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.

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

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

Erscheinungsdatum	25.10.2025
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	1-4704-7821-8 / 1470478218
ISBN-13	978-1-4704-7821-6 / 9781470478216
Zustand	Neuware