A spectral correspondence for Maaß waveforms
Artikel i vetenskaplig tidskrift, 1999

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.

spectral correspondence

quaternion orders

Fuchsian group

Maass forms


Stefan Lemurell

Göteborgs universitet

Institutionen för matematik, Matematik/Tillämpad matematik

Geometric and Functional Analysis

1016-443X (ISSN) 1420-8970 (eISSN)

Vol. 9 1128-1155