Introduction to Analytic and Probabilistic Number Theory

Häftad, Engelska, 2015

1 289 kr

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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.

Produktinformation

Utgivningsdatum2015-01-31
Mått178 x 254 x undefined mm
FormatHäftad
SpråkEngelska
SerieGraduate Studies in Mathematics
Antal sidor629
Upplaga3
FörlagAmerican Mathematical Society
ISBN9781470478216

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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