Umfang:
Online-Ressource (XVII, 163p, digital)
ISBN:
9783642052033
,
1282835629
,
9783642052026
,
9781282835627
Serie:
Lecture Notes of the Unione Matematica Italiana 8
Inhalt:
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.
Inhalt:
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.
Anmerkung:
Includes bibliographical references and index
,
Zeta Functions over Zeros of Zeta Functions; Preface; List of Special Symbols; 1 Introduction; 2 Infinite Products and Zeta-Regularization; 3 The Riemann Zeta Function (x): a Primer; 4 Riemann Zeros and Factorizations of the Zeta Function; 5 Superzeta Functions: an Overview; 6 Explicit Formulae; 7 The Family of the First Kind {Z(s -t)}; 8 The Family of the Second Kind { Z(-t) }; 9 The Family of the Third Kind { Z(s -)}; 10 Extension to Other Zeta- and L-Functions; 11 Application: an Asymptotic Criterion for the Riemann Hypothesis; A Numerical Explorations; B The Selberg Case
,
C On the Logarithmic Derivatives at 1 2D On the Zeros of the Zeta Function by Hj. Mellin (1917); References; Index; Editorial Policy;
Weitere Ausg.:
ISBN 9783642052026
Weitere Ausg.:
Buchausg. u.d.T. Voros, André Zeta functions over zeros of zeta functions Berlin : Springer, 2010 ISBN 9783642052026
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Zetafunktion
DOI:
10.1007/978-3-642-05203-3
URL:
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