Generalized Analytic Automorphic Forms in Hypercomplex Spaces

This book provides a comprehensive overview of the basic theory of hypercomplex-analytic automorphic forms and functions in higher dimensional spaces. It gives a summary on the research results obtained over the last five years and establishes a new field within the theory of functions of hypercomplex variables and within analytic number theory.

First extensive, comprehensive detailed and rather offrounded treatment of the basic theory of hypercomplex-analytic automorphic forms Summarizes recent research results on a new branch within hypercomplex analysis and analytic number theory Provides a breakthru in this research field and opens the door for further investigation in this line Includes useful perspectives for applications to function spaces and global analysis, as it develops new methods to tackle these problems

Klappentext

This book offers basic theory on hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Vector- and Clifford algebra-valued Eisenstein and Poincar series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. It establishes explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series, and introduces hypercomplex multiplication of lattices.

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