Zeta Functions over Zeros of Zeta Functions
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.

1139944705
Zeta Functions over Zeros of Zeta Functions
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.

49.95 In Stock
Zeta Functions over Zeros of Zeta Functions

Zeta Functions over Zeros of Zeta Functions

by André Voros
Zeta Functions over Zeros of Zeta Functions

Zeta Functions over Zeros of Zeta Functions

by André Voros

Overview

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.

Product Details

ISBN-13: 9783642052026
Publisher: Springer Berlin Heidelberg
Publication date: 12/17/2009
Series: Lecture Notes of the Unione Matematica Italiana , #8
Edition description: 2010
Pages: 163
Product dimensions: 6.10(w) x 9.10(h) x 0.60(d)

Table of Contents

Infinite Products and Zeta-Regularization.- The Riemann Zeta Function #x03B6;(): a Primer.- Riemann Zeros and Factorizations of the Zeta Function.- Superzeta Functions: an Overview.- Explicit Formulae.- The Family of the First Kind {#x2112; ( | )}.- The Family of the Second Kind.- The Family of the Third Kind.- Extension to Other Zeta- and -Functions.- Application: an Asymptotic Criterion for the Riemann Hypothesis.
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Science & Technology
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Number Theory
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