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Arithmetical Aspects of the Large Sieve Inequality

  • Olivier Ramaré
  • D. S. Ramana

Table of contents

  1. Front Matter
    Pages i-x
  2. Olivier Ramaré
    Pages 1-5
  3. Olivier Ramaré
    Pages 7-15
  4. Olivier Ramaré
    Pages 31-38
  5. Olivier Ramaré
    Pages 39-49
  6. Olivier Ramaré
    Pages 51-60
  7. Olivier Ramaré
    Pages 61-62
  8. Olivier Ramaré
    Pages 63-74
  9. Olivier Ramaré
    Pages 75-81
  10. Olivier Ramaré
    Pages 83-94
  11. Olivier Ramaré
    Pages 95-104
  12. Olivier Ramaré
    Pages 105-109
  13. Olivier Ramaré
    Pages 111-117
  14. Olivier Ramaré
    Pages 119-120
  15. Olivier Ramaré
    Pages 121-127
  16. Olivier Ramaré
    Pages 129-137
  17. Olivier Ramaré
    Pages 139-142
  18. Olivier Ramaré
    Pages 143-145
  19. Olivier Ramaré
    Pages 147-157
  20. Olivier Ramaré
    Pages 159-176
  21. Olivier Ramaré
    Pages 177-186
  22. Back Matter
    Pages 187-201

About this book

Introduction

This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved.

Authors and affiliations

  • Olivier Ramaré
    • 1
  1. 1.CNRSUniversité Lille 1France

Editors and affiliations

  • D. S. Ramana
    • 1
  1. 1.Harish-Chandra Research InstitueAllahabadIndia

Bibliographic information

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