Eisenstein series with non-unitary twists

Anton Deitmar; Frank Monheim

doi:10.4134/JKMS.j170042

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2018; 55(3): 507-530

Online first article April 10, 2018 Printed May 1, 2018

https://doi.org/10.4134/JKMS.j170042

Eisenstein series with non-unitary twists

Anton Deitmar, Frank Monheim

Mathematisches Institut, Mathematisches Institut

Abstract

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Abstract

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

Keywords: Eisenstein series, non-unitary representation, cusp-form

MSC numbers: 11F72, 11F75, 43A80