Zeta Functions over Zeros of Zeta Functions
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, whi...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2010, 2010
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| Edition: | 1st ed. 2010 |
| Series: | Lecture Notes of the Unione Matematica Italiana
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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