Introduction to Analytic and Probabilistic Number Theory (Graduate Studies in Mathematics 3rd Revised edition)
By: Gerald Tenenbaum (author)Hardback
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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 methodsSome tools from real analysisPrime numbersArithmetic functionsAverage ordersSieve methodsExtremal ordersThe method of van der CorputDiophantine approximationComplex analysis methodsThe Euler gamma functionGenerating functions: Dirichlet seriesSummation formulaeThe Riemann zeta functionThe prime number theorem and the Riemann hypothesisThe Selberg-Delange methodTwo arithmetic applicationsTauberian theoremsPrimes in arithmetic progressionsProbabilistic methodsDensitiesLimiting distributions of arithmetic functionsNormal orderDistribution of additive functions and mean values of multiplicative functionsFriable integersThe saddle-point methodIntegers free of small factorsBibliographyIndex
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- ID: 9780821898543
3rd Revised edition
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