Introduction to Analytic and Probabilistic Number Theory

Häftad, Engelska, 2015

Del i serien Graduate Studies in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-01-31
Mått:178 x 254 x undefined mm
Format:Häftad
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:629
Upplaga:3
Förlag:American Mathematical Society
ISBN:9781470478216

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Optimering inom Naturvetenskap och teknik

Mer om författaren

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

Recensioner i media

“The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate.” - Mathematical Reviews

Innehållsförteckning

Part I. Elementary methodsChapter I.0. Some tools from real analysisChapter I.1. Prime numbersChapter I.2. Arithmetic functionsChapter I.3. Average ordersChapter I.4. Sieve methodsChapter I.5. Extremal ordersChapter I.6. The method of van der CorputChapter I.7. Diophantine approximationPart II. Complex analysis methodsChapter II.0. The Euler gamma functionChapter II.1. Generating functions: Dirichlet seriesChapter II.2. Summation formulaeChapter II.3. The Riemann zeta functionChapter II.4. The prime number theorem and the Riemann hypothesisChapter II.5. The Selberg-Delange methodChapter II.6. Two arithmetic applicationsChapter II.7. Tauberian theoremsChapter II.8. Primes in arithmetic progressionsPart III. Probabilistic methodsChapter III.1. DensitiesChapter III.2. Limiting distributions of arithmetic functionsChapter III.3. Normal orderChapter III.4. Distribution of additive functions and mean values of multiplicative functionsChapter III.5. Friable integers. The saddle-point methodChapter III.6. Integers free of small factors