Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 8)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Zeta Functions over Zeros of Zeta Functions
Authors: André Voros
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-642-05203-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Softcover ISBN: 978-3-642-05202-6Published: 17 December 2009
eBook ISBN: 978-3-642-05203-3Published: 21 November 2009
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: XVII, 163
Topics: Number Theory, Functions of a Complex Variable, Approximations and Expansions