Zeta Functions of Groups and Rings

Zeta Functions of Groups and Rings PDF

Author: Marcus du Sautoy

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 217

ISBN-13: 354074701X

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Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Zeta Functions over Zeros of Zeta Functions

Zeta Functions over Zeros of Zeta Functions PDF

Author: André Voros

Publisher: Springer Science & Business Media

Published: 2009-11-21

Total Pages: 171

ISBN-13: 3642052037

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In this text, 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.

The semi-simple zeta function of quaternionic Shimura varieties

The semi-simple zeta function of quaternionic Shimura varieties PDF

Author: Harry Reimann

Publisher: Springer

Published: 2006-11-14

Total Pages: 152

ISBN-13: 354068414X

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This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.

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