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Mathematics - Number Theory and Discrete Mathematics | Zeta Functions over Zeros of Zeta Functions

Zeta Functions over Zeros of Zeta Functions

Voros, André

2010, XVII, 163p.

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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.

Content Level » Research

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

Related subjects » Analysis - Number Theory and Discrete Mathematics

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