Analytic Number Theory

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

  • J. B. Friedlander
  • D. R. Heath-Brown
  • H. Iwaniec
  • J. Kaczorowski
  • Alberto Perelli
  • Carlo Viola

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

Table of contents

  1. Front Matter
    Pages I-XI
  2. John B. Friedlander
    Pages 1-49
  3. D. R. Heath-Brown
    Pages 51-95
  4. Henryk Iwaniec
    Pages 97-132
  5. 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.


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

Authors and affiliations

  • J. B. Friedlander
    • 1
  • D. R. Heath-Brown
    • 2
  • H. Iwaniec
    • 3
  • J. Kaczorowski
    • 4
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Mathematical InstituteUniversity of OxfordOxfordEngland
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA
  4. 4.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznanPoland

Editors and affiliations

  • Alberto Perelli
    • 1
  • Carlo Viola
    • 2
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenovaItaly
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-36363-7
  • Online ISBN 978-3-540-36364-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site