3 papers
math.NT2019
On the Random Wave Conjecture for Dihedral Maaß Forms
Peter Humphries, Rizwanur Khan
We prove two results on arithmetic quantum chaos for dihedral Maass forms, both of which are manifestations of Berry's random wave conjecture: Planck scale mass equidistribution an…
math.NT2019
Test Vectors for Nonarchimedean Godement-Jacquet Zeta Integrals
Peter Humphries
Given an induced representation of Langlands type of with nonarchimedean, we show that there exist explicit choices of matrix coefficient and Sch…
math.NT2019
Motohashi's fourth moment identity for non-archimedean test functions and applications
Valentin Blomer, Peter Humphries, Rizwanur Khan +1
Motohashi established an explicit identity between the fourth moment of the Riemann zeta function weighted by some test function and a spectral cubic moment of automorphic L-functi…