Generalized Analytic Automorphic Forms in Hypercomplex Spaces / by Rolf Sören Krausshar
(Frontiers in Mathematics)
| データ種別 | 電子ブック |
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| 出版者 | Basel : Birkhäuser Basel |
| 出版年 | 2004 |
| 本文言語 | 英語 |
| 大きさ | XV, 168 p : online resource |
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| 内容注記 | Introduction 1. Function Theory in Hypercomplex Spaces 2. Clifford-analytic Eisenstein Series Associated to Translation Groups 3. Clifford-analytic Modular Forms Bibliography Index |
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| 一般注記 | 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 |
| 著者標目 | *Krausshar, Rolf Sören author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Integral transforms LCSH:Operational calculus LCSH:Potential theory (Mathematics) LCSH:Sequences (Mathematics) LCSH:Special functions LCSH:Number theory FREE:Mathematics FREE:Special Functions FREE:Integral Transforms, Operational Calculus FREE:Potential Theory FREE:Sequences, Series, Summability FREE:Number Theory |
| 分 類 | DC23:515.5 |
| 巻冊次 | ISBN:9783764378042 
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| ISBN | 9783764378042 |
| URL | http://dx.doi.org/10.1007/b95203 |
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