32 citations · 177 across the 24 of their papers we have counts for
4 papers · 1 filter
Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics
Peter Humphries, Maksym Radziwiłł
We asymptotically estimate the variance of the number of lattice points in a thin, randomly rotated annulus lying on the surface of the sphere. This partially resolves a conjecture…
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…
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…
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…