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Selberg zeta and theta functions : a differential operator approach

Author: Ulrich Bunke; Martin Olbrich
Publisher: Berlin : Akademie Verlag ; New York : VCH, ©1995.
Series: Mathematical research, Bd. 83.
Edition/Format:   Print book : English : 1st edView all editions and formats
Summary:

A comprehensive exposition of the theory of Selberg zeta and theta functions for bundles on compact locally symmetric spaces of rank 1. The connection between these functions and the spectrum of  Read more...

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Additional Physical Format: Online version:
Bunke, Ulrich, 1963-
Selberg zeta and theta functions.
Berlin : Akademie Verlag ; New York : VCH, ©1995
(OCoLC)625165280
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ulrich Bunke; Martin Olbrich
ISBN: 3055016904 9783055016905
OCLC Number: 32511877
Description: 168 pages : illustrations ; 24 cm.
Contents: 1. Elliptic Operators, Duality, and Trace Formulas. 1.1. Bundles and operators. 1.2. Wave kernels and duality. 1.3. Harmonic analysis on compact symmetric spaces. 1.4. The trace formula --
2. Theta Functions. 2.1. Theta functions for compact locally symmetric rank-one spaces. 2.2. Theta functions for surfaces with cusps --
3. The Selberg Zeta Function. 3.1. Zeta functions and the geodesic flow. 3.2. Traces of resolvents. 3.3. Properties of the Selberg zeta function --
4. The Ruelle Zeta Function. 4.1. The functional equations. 4.2. The behaviour at the central point --
5. Examples. 5.1. The function case. 5.2. Spinors on real hyperbolic manifolds. 5.3. Differential forms on real and complex hyperbolic manifolds. 5.4. One-forms on quaternionic hyperbolic manifolds --
6. Alternative Descriptions of the Singularities. 6.1. Dynamical Lefschetz formulas. 6.2. Group cohomology of the principal series.
Series Title: Mathematical research, Bd. 83.
Responsibility: Ulrich Bunke, Martin Olbrich.

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