Author	Krausshar, Rolf Sรถren. author
Title	Generalized Analytic Automorphic Forms in Hypercomplex Spaces [electronic resource] / by Rolf Sรถren Krausshar
Imprint	Basel : Birkhรคuser Basel, 2004
Connect to	http://dx.doi.org/10.1007/b95203
Descript	XV, 168 p. online resource

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 Poincarรฉ 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

Introduction -- 1. Function Theory in Hypercomplex Spaces -- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups -- 3. Clifford-analytic Modular Forms -- Bibliography -- Index

1. Mathematics
2. Integral transforms
3. Operational calculus
4. Potential theory (Mathematics)
5. Sequences (Mathematics)
6. Special functions
7. Number theory
8. Mathematics
9. Special Functions
10. Integral Transforms
11. Operational Calculus
12. Potential Theory
13. Sequences
14. Series
15. Summability
16. Number Theory