works on
central values 1character groups 1dirichlet l-functions 1moments of L-functions 1prime moduli 1

From the 1 of 4 linked papers with an AI index.

collaborators

4 papers

math.NT2026

The First Moment of Dirichlet L-functions over Generators of the Character Group

Rizwanur Khan

The paper computes the average (first moment) of the central values L(1/2,χ) for Dirichlet characters χ that generate the full character group modulo a prime q, as q grows.

math.NT2025

-Norm Bounds for Automorphic Forms via Spectral Reciprocity

Peter Humphries, Rizwanur Khan

Let be a Hecke-Maass cusp form on the modular surface , namely an -normalised nonconstant Laplacian eigenfunction on ${\rm SL}_…

math.NT2025

On moments of L-functions over Dirichlet characters

Avery Bainbridge, Rizwanur Khan, Ze Sen Tang

We give a new proof of Heath-Brown's full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first…

math.NT2025

The Second Moment of Rankin-Selberg -Functions in Conductor-Dropping Regimes

Peter Humphries, Rizwanur Khan

We prove an asymptotic formula for the second moment of -functions associated to the Rankin-Selberg convolution of two holomorphic Hecke cusp forms with equal weight.