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＜E-Book＞
Zeta Functions over Zeros of Zeta Functions / by André Voros
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 8)

Edition	1st ed. 2010.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2010
Language	English
Size	XVII, 163 p : online resource
Authors	*Voros, André author SpringerLink (Online service)
Subjects	LCSH:Number theory LCSH:Functions of complex variables LCSH:Approximation theory FREE:Number Theory FREE:Functions of a Complex Variable FREE:Approximations and Expansions
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-05203-3

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