Analytic Number Theory (COLLOQUIUM PUBLICATIONS (AMER MATHEMATICAL SOC))

Iwaniec, Henryk

ISBN 10: 0821836331 / ISBN 13: 9780821836330

Published by Amer Mathematical Society, 2004

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Bibliographic Details

• Title: Analytic Number Theory (COLLOQUIUM PUBLICATIONS (AMER MATHEMATICAL SOC))
• Publisher: Amer Mathematical Society
• Publication Date: 2004
• Language: English
• ISBN 10: 0821836331
• ISBN 13: 9780821836330
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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.

From the Back Cover

The four contributions collected in this volume deal with several advanced results in analytic number theory. Friedlander’s paper contains some recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials. Heath-Brown's lecture notes mainly deal with counting integer solutions to Diophantine equations, using among other tools several results from algebraic geometry and from the geometry of numbers. Iwaniec’s paper gives a broad picture of the theory of Siegel’s zeros and of exceptional characters of L-functions, and gives a new proof of Linnik’s theorem on the least prime in an arithmetic progression. Kaczorowski’s article presents an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg, with a detailed exposition of several recent results.