Fourier expansions of vector-valued automorphic functions with non-unitary twists
Artikel i vetenskaplig tidskrift, 2023

We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility or unitarity are made. Examples of such eigenfunctions include vector-valued twisted automorphic forms of Fuchsian groups. We further provide a detailed description of the Fourier coefficients and explicitly identify each of their constituents, which intimately depend on the eigenvalues of the twisting endomorphism and the size of its Jordan blocks. In addition, we determine the growth properties of the Fourier coefficients.

twisted automorphic function

generalized automorphic function

Fourier expansion

non-unitary representation


Ksenia Fedosova

Albert-Ludwigs-Universität Freiburg

Anke Pohl

Universität Bremen

Julie Rowlett

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Communications in Number Theory and Physics

1931-4523 (ISSN) 1931-4531 (eISSN)

Vol. 17 1 173-248

Geometrisk analys och tillämpningar i mikrobekologi

Vetenskapsrådet (VR) (2018-03873), 2019-01-01 -- 2022-12-31.


Algebra och logik


Matematisk analys



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