Lecture Notes of the Unione Matematica Italiana

Zeta Functions over Zeros of Zeta Functions

Authors: Voros, André

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eBook 29,74 €
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  • ISBN 978-3-642-05203-3
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Softcover 36,35 €
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  • ISBN 978-3-642-05202-6
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About this book

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.

Reviews

From the reviews:

“The book is written in a pleasant style, with short chapters, each explaining a single topic. … This book is a very timely synthesis of the results that have been scattered in the literature up to now. It gives a systematic overview and adds the discoveries of the author (with collaborators). … this book will prove to be an important step in the further development of the subject of superzeta functions.”­­­ (Machiel van Frankenhuijsen, Mathematical Reviews, Issue 2010 j)

“The book is very carefully written and presents an object of research which has been investigated for many decades but never treated in such a comprehensive manner. A valuable contribution to the field of analytic number theory.” (Anton Deitmar, Zentralblatt MATH, Vol. 1206, 2011)


Table of contents (11 chapters)

  • Introduction

    Voros, André

    Pages 1-8

    Preview Buy Chapter 30,19 €
  • Infinite Products and Zeta-Regularization

    Voros, André

    Pages 9-22

    Preview Buy Chapter 30,19 €
  • The Riemann Zeta Function ζ(x): a Primer

    Voros, André

    Pages 23-31

    Preview Buy Chapter 30,19 €
  • Riemann Zeros and Factorizations of the Zeta Function

    Voros, André

    Pages 33-40

    Preview Buy Chapter 30,19 €
  • Superzeta Functions: an Overview

    Voros, André

    Pages 41-47

    Preview Buy Chapter 30,19 €

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-642-05203-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,35 €
price for Spain (gross)
  • ISBN 978-3-642-05202-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Zeta Functions over Zeros of Zeta Functions
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
8
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-05203-3
DOI
10.1007/978-3-642-05203-3
Softcover ISBN
978-3-642-05202-6
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XVII, 163
Topics