Generalized Analytic Automorphic Forms in Hypercomplex Spaces

By: Rolf S. Krausshar

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Paperback | 1 October 2007

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188 Pages

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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 Poincare 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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Introduction
Function Theory in Hypercomplex Spaces
Clifford-analytic Eisenstein Series Associated to Translation Groups
Clifford-analytic Modular Forms
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Generalized Analytic Automorphic Forms in Hypercomplex Spaces

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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