Zeta Functions over Zeros of Zeta Functions

• Main Author: Voros, André (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes of the Unione Matematica Italiana, 8
• Subjects: Mathematics.; Approximation theory.; Functions of complex variables.; Number theory.; Number Theory.; Functions of a Complex Variable.; Approximations and Expansions.
• Physical Description: XVII, 163 p. online resource.
• ISBN: 9783642052033
• ISSN: 1862-9113 ;

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.