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.
newforms
theta-series
algebras
Hecke congruence groups
Hecke operators
Selberg trace formula
orders
Newforms
Maass waveforms
Mathematics
Author
T. R. Blackman
Massachusetts Institute of Technology
Stefan Lemurell
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Journal of Number Theory
0022-314X (ISSN) 1096-1658 (eISSN)
Vol. 158 1-22Subject Categories (SSIF 2011)
Mathematics
Roots
Basic sciences
DOI
10.1016/j.jnt.2015.05.017