A spectral correspondence for Maass waveforms
Spectral Theory
2007-05-23 v1 Number Theory
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.
Cite
@article{arxiv.math/9805018,
title = {A spectral correspondence for Maass waveforms},
author = {Jens Bolte and Stefan Johansson},
journal= {arXiv preprint arXiv:math/9805018},
year = {2007}
}
Comments
22 pages