Generalized Analytic Automorphic Forms in Hypercomplex Spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2004
|
| Series: | Frontiers in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 Poincaré 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 |
| Physical Description: | 1 Online-Ressource (XV, 168 p) |
| ISBN: | 9783764378042 9783764370596 |
| ISSN: | 1660-8046 |
| DOI: | 10.1007/b95203 |
Staff View
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783764378042 9783764370596 |
| issn | 1660-8046 |
| language | English |
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| physical | 1 Online-Ressource (XV, 168 p) |
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| publishDate | 2004 |
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| spelling | Krausshar, Rolf Sören Verfasser aut Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar Basel Birkhäuser Basel 2004 1 Online-Ressource (XV, 168 p) txt rdacontent c rdamedia cr rdacarrier Frontiers in Mathematics 1660-8046 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 Poincaré 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 Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd rswk-swf Hardy-Raum (DE-588)4159109-4 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s 1\p DE-604 Hardy-Raum (DE-588)4159109-4 s 2\p DE-604 https://doi.org/10.1007/b95203 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Krausshar, Rolf Sören Generalized Analytic Automorphic Forms in Hypercomplex Spaces Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| subject_GND | (DE-588)4003972-9 (DE-588)4159109-4 |
| title | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_auth | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_exact_search | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_full | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_fullStr | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_full_unstemmed | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_short | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_sort | generalized analytic automorphic forms in hypercomplex spaces |
| topic | Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| topic_facet | Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form Hardy-Raum |
| url | https://doi.org/10.1007/b95203 |
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