A spectral correspondence for Maass waveforms

Jens Bolte; Stefan Johansson

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A spectral correspondence for Maass waveforms

Jens Bolte·Stefan Johansson

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Abstract

Let O^1 be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order O in an indefinite quaternion division algebra over Q. Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for O^1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian defined on the Maass newforms for the Hecke congruence group Gamma_0(d), when d is the discriminant of the maximal order O. We also show the equality of the traces of certain Hecke operators defined on the Laplace eigenspaces for O^1 and the newforms of level d, respectively.

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Jens Bolte, Stefan Johansson. 1998-05-05. A spectral correspondence for Maass waveforms. https://arxiv.org/abs/math/9805018

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