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A spectral correspondence for Maaß waveforms

Stefan Lemurell (Institutionen för matematik, Matematik/Tillämpad matematik)
Geom. Funct. Anal. (1016-443X). Vol. 9 (1999), 6, p. 1128-1155.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Maass forms, Fuchsian group, quaternion orders, spectral correspondence

Co-author: Jens Bolte Published under Stefan Lemurell's former family name Johansson.

Denna post skapades 2007-10-03. Senast ändrad 2015-12-17.
CPL Pubid: 51026


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Institutioner (Chalmers)

Institutionen för matematik, Matematik/Tillämpad matematik (1987-2001)


Algebra och geometri

Chalmers infrastruktur