Zeta Functions over Zeros of Zeta Functions

• Κύριος συγγραφέας: Voros, André (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Σειρά: Lecture Notes of the Unione Matematica Italiana, 8
• Θέματα: Mathematics.; Approximation theory.; Functions of complex variables.; Number theory.; Number Theory.; Functions of a Complex Variable.; Approximations and Expansions.

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...

Πίνακας περιεχομένων:

• 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.