Generalized analytic automorphic forms in hypercomplex spaces /
This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimens...
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| Format: | eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser Verlag,
[2004]
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| Series: | Frontiers in mathematics (Springer-Verlag)
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincar series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xv, 167 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages [151]-161). |
| ISBN: | 9783764378042 (electronic bk.) 3764378042 (electronic bk.) |
| ISSN: | 1660-8046 |