ENGLISH

Analytic Number Theory: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11–18, 2002

By D. R. Heath-Brown , J. B. Friedlander , H. Iwaniec , J. Kaczorowski (auth.) , Alberto Perelli , Carlo Viola (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2006
ISBN
978-3-540-36363-7, 978-3-540-36364-4
DOI
10.1007/3-540-36363-7
Language
english
Format
PDF
Filesize
3 MB (3117380 bytes)
Series
Lecture Notes in Mathematics 1891
Edition
1
Pages
217\223
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Number Theory; Algebraic Geometry

Description

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.

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