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Equidistribution in Number Theory, An Introduction

  • Conference proceedings
  • © 2007

Overview

Editors:
  1. Andrew Granville

    1. University of Montréal, QC,, Canada

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    You can also search for this editor in PubMed   Google Scholar

  2. Zeév Rudnick

    1. Tel-Aviv University, Israel

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    You can also search for this editor in PubMed   Google Scholar

  • Focus on distribution questions in number theory
  • Very broad view of the emergence of this exciting new school of thought
  • Motivated surveys of up-to-date research by truly leading researchers
  • Detailed introductions to key subjects from outstanding expositors

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 237)

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Table of contents (15 papers)

  1. Front Matter

    Pages I-XV
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  2. UNIFORM DISTRIBUTION

    • Andrew Granville, Zeév Rudnick
    Pages 1-13

  3. SIEVING AND THE ERDŐS–KAC THEOREM

    • Andrew Granville, K. Soundararajan
    Pages 15-27

  4. UNIFORM DISTRIBUTION, EXPONENTIAL SUMS, AND CRYPTOGRAPHY

    • John B. Friedlander
    Pages 29-57

  5. THE DISTRIBUTION OF PRIME NUMBERS

    • K. Soundararajan
    Pages 59-83

  6. TORSION POINTS ON CURVES

    • Andrew Granville, Zeév Rudnick
    Pages 85-92

  7. THE DISTRIBUTION OF ROOTS OF A POLYNOMIAL

    • Andrew Granville
    Pages 93-102

  8. MANIN–MUMFORD, ANDRÉ–OORT, THE EQUIDISTRIBUTION POINT OF VIEW

    • Emmanuel Ullmo
    Pages 103-138

  9. ANALYTIC METHODS FOR THE DISTRIBUTION OF RATIONAL POINTS ON ALGEBRAIC VARIETIES

    • D. R. Heath-Brown
    Pages 139-168

  10. UNIVERSAL TORSORS OVER DEL PEZZO SURFACES AND RATIONAL POINTS

    • Ulrich Derenthal, Yuri Tschinkel
    Pages 169-196

  11. AN INTRODUCTION TO THE LINNIK PROBLEMS

    • W. Duke
    Pages 197-216

  12. DISTRIBUTION MODULO ONE AND RATNER’S THEOREM

    • Jens Marklof
    Pages 217-244

  13. SPECTRAL THEORY OF AUTOMORPHIC FORMS: A VERY BRIEF INTRODUCTION

    • A. Venkatesh
    Pages 245-260

  14. SOME EXAMPLES HOWTO USE MEASURE CLASSIFICATION IN NUMBER THEORY

    • Elon Lindenstrauss
    Pages 261-303

  15. AN INTRODUCTION TO QUANTUM EQUIDISTRIBUTION

    • S. De Bièvre
    Pages 305-330

  16. THE ARITHMETIC THEORY OF QUANTUM MAPS

    • Zeév Rudnick
    Pages 331-342

  17. Back Matter

    Pages 343-345
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Keywords

About this book

From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series “Seminaire ´ de mathematiques ´ superieures”, ´ was held at the U- versite ´ de Montreal, ´ on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have noticed incre- ing interest being paid to distribution problems, whether of rational points, of zeros of zeta functions, of eigenvalues, etc. Although these problems have been motivated from very di?erent perspectives, one nds that there is much in common, and presumably it is healthy to try to view such questions as part of a bigger subject. It is for this reason we decided to hold a school on “Equidistribution in number theory” to introduce junior researchers to these beautiful questions, and to determine whether di?erent approaches can in uence one another. There are far more good problems than we had time for in our schedule. We thus decided to focus on topics that are clearly inter-related or do not requirealotofbackgroundtounderstand.

Editors and Affiliations

  • University of Montréal, QC,, Canada

    Andrew Granville

  • Tel-Aviv University, Israel

    Zeév Rudnick

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