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Zeta Functions over Zeros of Zeta Functions

  • André Voros

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 8)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. André Voros
    Pages 1-8
  3. André Voros
    Pages 41-47
  4. André Voros
    Pages 49-58
  5. André Voros
    Pages 91-111
  6. Back Matter
    Pages 153-164

About this book

Introduction

The famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These ‘second-generation’ zeta functions have surprisingly many explicit, yet largely unnoticed properties, which are surveyed here in an accessible and synthetic manner, and then compiled in numerous tables. No previous book has addressed this neglected topic in analytic number theory. Concretely, this handbook will help anyone faced with symmetric sums over zeros like Riemann’s. More generally, it aims at reviving the interest of number theorists and complex analysts toward those unfamiliar functions, on the 150th anniversary of Riemann’s work.

Keywords

L-functions Mellin transforms Prime Riemann Zeros Riemann zeta function Zeta Functions Zeta-regularization number theory

Authors and affiliations

  • André Voros
    • 1
  1. 1.Institut de Physique Theorique (IPHT)CEA SaclayGif sur YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-05203-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-05202-6
  • Online ISBN 978-3-642-05203-3
  • Series Print ISSN 1862-9113
  • Buy this book on publisher's site
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