Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Ksenia Fedosova (Albert-Ludwigs-Universität Freiburg)
In this talk, we investigate the behavior of the Eisenstein series, or generalized eigenfunctions of the Laplace operator on hyperbolic surfaces. We twist them by a (possibly) non-unitary representation of the fundamental group of the manifold, show their convergence on some half-plane and study their Fourier expansion.Further, we show the convergence and meromorphic continuation of the Selberg zeta function twisted by the same type ofrepresentations.