Analytic Number Theory

Häftad, Engelska, 2004

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Beskrivning

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques.The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercises in each section serve a dual purpose, with some intended to improve the reader's understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much necessary information about them included in two survey chapters.

Produktinformation

Utgivningsdatum:2004-07-30
Vikt:0 g
Format:Häftad
Språk:Engelska
Serie:Colloquium Publications
Antal sidor:615
Förlag:American Mathematical Society
ISBN:9781470467708

Utforska kategorier

Talteori inom Naturvetenskap och teknik

Mer om författaren

Henryk Iwaniec, Rutgers University, Piscataway, NJ.Emmanuel Kowalski, Universite Bordeaux I, Talence, France.

Recensioner i media

The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" —Zentralblatt Math

Innehållsförteckning

IntroductionArithmetic functionsElementary theory of prime numbersCharactersSummation formulasClassical analytic theory of $L$-functionsElementary sieve methodsBilinear forms and the large sieveExponential sumsThe Dirichlet polynomialsZero-density estimatesSums over finite fieldsCharacter sumsSums over primesHolomorphic modular formsSpectral theory of automorphic formsSums of Kloosterman sumsPrimes in arithmetic progressionsThe least prime in an arithmetic progressionThe Goldbach problemThe circle methodEquidistributionImaginary quadratic fieldsEffective bounds for the class numberThe critical zeros of the Riemann zeta functionThe spacing of zeros of the Riemann zeta-functionCentral values of $L$-functionsBibliographyIndex