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Eisenstein series twisted with non-expanding cusp monodromies

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Fedosova,  Ksenia
Max Planck Institute for Mathematics, Max Planck Society;

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Pohl,  Anke D.
Max Planck Institute for Mathematics, Max Planck Society;

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Fedosova, K., & Pohl, A. D. (2020). Eisenstein series twisted with non-expanding cusp monodromies. The Ramanujan Journal, 51(3), 649-670. doi:10.1007/s11139-019-00205-5.


Cite as: https://hdl.handle.net/21.11116/0000-0006-0BFF-0
Abstract
Let $\Gamma$ be a geometrically finite Fuchsian group and suppose that $\chi\colon\Gamma\to\mathrm{GL}(V)$ 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.