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Higher order invariants in the case of compact quotients

Anton Deitmar — 2011

Open Mathematics

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.

Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar — 2014

Open Mathematics

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

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