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Let $Gamma$ be a geometrically finite Fuchsian group and suppose that $chicolonGammatomathrm{GL}(V)$ is a finite-dimensional representation with non-expanding cusp monodromy. We show that the parabolic Eisenstein series for $Gamma$ with twist $chi$ converges on some half-plane. Further, we develop Fourier-type expansions for these Eisenstein series.
We initiate the study of Selberg zeta functions $Z_{Gamma,chi}$ for geometrically finite Fuchsian groups $Gamma$ and finite-dimensional representations $chi$ with non-expanding cusp monodromy. We show that for all choices of $(Gamma,chi)$, the Selber
Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the sett
We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity properties of i
We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for its low-
We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adel