Spectral correspondences for Maass waveforms on quaternion groups
Journal article, 2016
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.
orders
Selberg trace formula
Mathematics
algebras
theta-series
newforms
Hecke congruence groups
Newforms
Hecke operators
Maass waveforms
Author
T. R. Blackman
Massachusetts Institute of Technology (MIT)
Stefan Lemurell
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Journal of Number Theory
0022-314X (ISSN) 1096-1658 (eISSN)
Vol. 158 1-22Subject Categories
Mathematics
Roots
Basic sciences
DOI
10.1016/j.jnt.2015.05.017