Equidistribution in Number Theory, An Introduction

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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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.

• Chemistry
• Mathematics
• NATO
• Physics
• Prime
• Prime number
• Science
• Series II
• algebraic varieties
• calculus
• cryptography
• number theory
• quantum chaos

• University of Montréal, QC,, Canada

  Andrew Granville

• Tel-Aviv University, Israel

  Zeév Rudnick

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