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 |

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 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

CONTENT

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

Mathematics
Integral transforms
Operational calculus
Potential theory (Mathematics)
Sequences (Mathematics)
Special functions
Number theory
Mathematics
Special Functions
Integral Transforms Operational Calculus
Potential Theory
Sequences Series Summability
Number Theory