Introduction to Analytic and Probabilistic Number Theory

Gerald Tenenbaum (Autor)

Buch | Hardcover

629 Seiten

2015 | Third Edition
American Mathematical Society (Verlag)
978-0-8218-9854-3 (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.

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

Erscheint lt. Verlag	30.8.2015
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	1280 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-8218-9854-X / 082189854X
ISBN-13	978-0-8218-9854-3 / 9780821898543
Zustand	Neuware