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＜電子ブック＞
Zeta Functions over Zeros of Zeta Functions / by André Voros
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 8)

版	1st ed. 2010.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2010
本文言語	英語
大きさ	XVII, 163 p : online resource
著者標目	*Voros, André author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Functions of complex variables LCSH:Approximation theory FREE:Number Theory FREE:Functions of a Complex Variable FREE:Approximations and Expansions
一般注記	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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