Monogenic Modular Forms in Two and Several Real and Complex Vector Variables

Abstract

In this paper we deal with monogenic and k-monogenic Clifford-valued automorphic forms in two and several vector variables. We focus on the construction of several families of Eisenstein and Poincare series within the setting of this function theory. The functions that we construct provide non-trivial examples for generalizations of the classical Hilbert modular forms within the framework of real and complex Clifford analysis.