On a new type of hypercomplex-analytic modular forms and their
relation to Maass wave forms.
Sören Krausshar (K.U.Leuven)
In this talk we deal with a new type of automorphic forms on arithmetic
subgroups of the Ahlfors Vahlen group. The setting is upper half-space in
Rn . The automorphic forms considered are in general Clifford algebra valued and they are null-solutions to higher dimensional generalizations of the
Cauchy-Riemann operator. We give explicit constructions for Eisensteinand Poincare series in this context. We further exhibit explicit relations to
higher dimensional variants of the Riemann zeta function and to multiple
divisor sums. Furthermore we explain how this theory of Clifford-analytic
automorphic forms fit within the framework of Maass wave forms. These are
eigenfunctions to the hyperbolic Laplace Beltrami operator on upper halfspace.
1