1998/05/05 by Jens Bolte, Stefan Johansson, Bolte, Jens +1
Decision Sciences · Mathematics · Physics and Astronomy · #11F12 #11F32 (Secondary) #11F72 (Primary) #30F35 #FOS: Mathematics #Number Theory (math.NT) #Scientific Measurement and Uncertainty Evaluation #Spectral Theory (math.SP) #Statistical Mechanics and Entropy #math.NT #math.SP #msc:11F12 #msc:11F32 #msc:11F72 #msc:30F35
paper · pdf · doi:10.48550/arxiv.math/9805018
22 pages
arxiv created 1998/05/05 · openalex publication_date 1998/05/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let O1 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 O1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian defined on the Maass newforms for the Hecke congruence group Gamma0(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 O1 and the newforms of level d, respectively.