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.
algebras
Selberg trace formula
Mathematics
Hecke operators
Newforms
Maass waveforms
Hecke congruence groups
orders
theta-series
newforms
Author
T. R. Blackman
Massachusetts Institute of Technology (MIT)
Stefan Lemurell
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
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