MPEJ Volume 7, No. 1, 18pp.
Received: May 31, 2001. Accepted: Sep 26, 2001.
Mayer D., Neunhaeuserer J.
An isomorphism between polynomial eigenfunctions of the transfer
operator and the Eichler cohomology for modular groups
ABSTRACT: For the group $PSL(2,\Z)$ it is known that there is an
isomorphism between polynomial eigenfunctions of the transfer operator
for the geodetic flow and the Eichler cohomology in number theory, see
\cite{[CM3]}, \cite{[LW]}, \cite{[LZ]}. In \cite{[CM3]} it is
indicated that such an isomorphism exists as well for the subgroups
$\Gamma(2)$ and $\Gamma_{0}(2)$ of $PSL(2,\Z)$. We will prove this and
provide some evidence by computer aided algebraic calculations that
such an isomorphism exists for all principal congruence subgroups
$\Gamma(N)$ and all congruence subgroups of Hecke type
$\Gamma_{0}(N)$.