ENGLISH

Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory

By Juergen Elstrodt , Fritz Grunewald , Jens Mennicke

Book information

Publisher
Springer
Year
1997
ISBN
9783540627456, 3540627456
LCC
QA320 .E47 1998
Open Library ID
OL691568M
Language
english
Format
PDF
Filesize
21 MB (22495003 bytes)
Series
Springer Monographs in Mathematics
Edition
1
Pages
272\272
Time added
2010-05-17 00:23:50

Description

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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