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  • © 2006

Analytic Number Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1891)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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  • ISBN: 978-3-540-36364-4
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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XI
  2. Producing Prime Numbers via Sieve Methods

    • John B. Friedlander
    Pages 1-49
  3. Counting Rational Points on Algebraic Varieties

    • D. R. Heath-Brown
    Pages 51-95
  4. Conversations on the Exceptional Character

    • Henryk Iwaniec
    Pages 97-132
  5. Axiomatic Theory of L-Functions: the Selberg Class

    • Jerzy Kaczorowski
    Pages 133-209
  6. Back Matter

    Pages 211-216

About this book

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.

Keywords

  • Diophantine equations
  • L-functions
  • Prime
  • Prime number
  • algebraic varieties
  • number theory
  • primes in progressions
  • rational points on varieties
  • sieve theory

Authors, Editors and Affiliations

  • Dipartimento di Matematica, Università di Genova, Genova, Italy

    Alberto Perelli

  • Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Carlo Viola

  • Department of Mathematics, University of Toronto, Toronto, Canada

    J. B. Friedlander

  • Mathematical Institute, University of Oxford, Oxford, England

    D. R. Heath-Brown

  • Department of Mathematics, Rutgers University, Piscataway, USA

    H. Iwaniec

  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznan, Poland

    J. Kaczorowski

Bibliographic Information

  • Book Title: Analytic Number Theory

  • Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002

  • Authors: J. B. Friedlander, D. R. Heath-Brown, H. Iwaniec, J. Kaczorowski

  • Editors: Alberto Perelli, Carlo Viola

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/3-540-36363-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Softcover ISBN: 978-3-540-36363-7

  • eBook ISBN: 978-3-540-36364-4

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 217

  • Topics: Number Theory, Algebraic Geometry

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-36364-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.95
Price excludes VAT (USA)