Theta series of quaternary quadratic forms over Z and Z[(1 + √p)/2]
The Local Converse Problem is to determine how the family of the local gamma factors characterizes the isomorphism class of an irreducible admissible generic representation of , with a non-archimedean local field, where runs through all irreducible supercuspidal representations of and runs through positive integers. The Jacquet conjecture asserts that it is enough to take . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...
In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2() with being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.