Terrence Blackman et. al.: “Spectral correspondences for Maass waveforms on quaternion groups”
“Spectral correspondences for Maass waveforms on quaternion groups” by Terrence Blackman and Stefan Lemurell has been peer reviewed and accepted for publication by the Journal of Number Theory, available for download 7 July 2015.
The work was supported by the MIT Mathematics Department and by the MIT Dr. Martin Luther King Jr. Visiting Professors & Scholars Program.
We prove that in most cases the Jacquet-Langlands correspondence between newforms for Hecke congruence groups and newforms for quaternion orders is a bijection. Our proof covers almost all cases where the Hecke congruence group is of cocompact type, i.e. when a bijection is possible. The proof uses the Selberg trace formula.