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Analytic number theory : lectures given at the C.I.M.E. summer school held in Cetraro, Italy, July 11-18, 2002 / J.B. Friedlander [and others] ; editors, A. Perelli, C. Viola.

Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1891.Publication details: Berlin : Springer ; Firenze : Fondazione C.I.M.E., 2006.Description: 1 online resource (xi, 212 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 3540363637
  • 9783540363637
  • 9783540363644
  • 3540363645
  • 9786611103392
  • 6611103392
Subject(s): Genre/Form: Additional physical formats: Print version:: Analytic number theory.DDC classification:
  • 512.7/3 22
LOC classification:
  • QA3 .L28 no.1891
Other classification:
  • 31.14
  • O156
Online resources:
Contents:
Producing Prime Numbers via Sieve Methods -- Counting Rational Points on Algebraic Varieties -- Conversations on the Exceptional Character -- Axiomatic Theory of L-Functions: the Selberg Class.
Summary: 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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Includes bibliographical references.

Print version record.

Producing Prime Numbers via Sieve Methods -- Counting Rational Points on Algebraic Varieties -- Conversations on the Exceptional Character -- Axiomatic Theory of L-Functions: the Selberg Class.

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.

English.

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