Introduction to Analytic and Probabilistic Number Theory
American Mathematical Society (Verlag)
978-0-8218-9854-3 (ISBN)
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 |
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Reihe/Serie | Graduate Studies in Mathematics |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 1280 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
Naturwissenschaften ► Physik / Astronomie | |
ISBN-10 | 0-8218-9854-X / 082189854X |
ISBN-13 | 978-0-8218-9854-3 / 9780821898543 |
Zustand | Neuware |
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