Weighted central limit theorems for central values of L-functions

Hung Bui, Natalie Evans, Stephen Lester*, Kyle Pratt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We establish a central limit theorem for the central values of Dirichlet $L$-functions with respect to a weighted measure on the set of primitive characters modulo $q$ as $q \rightarrow \infty$. Under the Generalized Riemann Hypothesis (GRH), we also prove a weighted central limit theorem for the joint distribution of the central $L$-values corresponding to twists of two distinct primitive Hecke eigenforms. As applications, we obtain (under GRH) positive proportions of twists for which the central $L$-values simultaneously grow or shrink with $q$ as well as a positive proportion of twists for which linear combinations of the central $L$-values are nonzero.
Original languageEnglish
JournalJournal of the European Mathematical Society
Publication statusAccepted/In press - 11 Oct 2023

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