4. FHST-Meeting on Geometry and Analysis
Freiburg-Heidelberg-Stuttgart-Heidelberg
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Ksenia Fedosova: Fourier expansions of vector-valued automorphic functions
In this talk, I 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 will
discuss 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.
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