Clifford Algebras: Application to Mathematics, Physics, and Engineering pages:75-90
6th international conference on Clifford algebras and their applications in mathematical physics location:Cookeville, TN, USA date:20-25 May 2002
In this paper we deal with higher dimensional Clifford-valued generalizations of several families of classical complex-analytic Eisenstein series and Poincare series to the framework of Clifford analysis.
The function series that we discuss provide non-trivial examples of Clifford-valued functions that are in the kernel of Dirac operators, or more general, in function classes of $k$-monogenic functions, which show a quasi-invariant behavior under special discrete subgroups of the Vahlen group. In particular, we construct Eisenstein and Poincare series in the Clifford analysis setting in one and two hypercomplex variables that are invariant under higher dimensional generalizations of the classical modular group.