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Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory

Posted on 2010-03-16




Name:Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory
ASIN/ISBN:3540627456
Language:English
File size:21 Mb
Publish Date: 1997
ISBN: 3540627456
Pages: 524 pages
File Type: PDF
File Size: 21 MB
Other Info: Springer
   Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory

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Juergen Elstrodt, Fritz Grunewald, Jens Mennicke, ""

This book deals with a broad range of topics from the theory of automorphic functions on three-dimensional hyperbolic space and its arithmetic group theoretic and geometric ramifications. Starting off with several models of hyperbolic space and its group of motions the authors discuss the spectral theory of the Laplacian and Selberg's theory for cofinite groups. This culminates in explicit versions of the Selberg trace formula and the Selberg zeta-function. The interplay with arithmetic is demonstrated by means of the groups PSL(2) over rings and of quadratic integers, their Eisenstein series and their associated Hermitian forms. A rich chapter on concrete examples of arithmetic and non-arithmetic cofinite groups enhances the usefulness of this work for a wide circle of mathematicians.

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