Year: 2017
Type: preprint
Abstract: We extend the work of Fouvry, Kowalski and Michel on correlation between Hecke eigenvalues of modular forms and algebraic trace functions in order to establish an asymptotic formula for a generalized cubic moment of modular L-functions at the central point s = 1/2 and for prime moduli q. As an application, we exploit our recent result on the mollification of the fourth moment of Dirichlet L-functions to derive that for any pair $(ω_1,ω_2)$ of multiplicative characters modulo q, there is a positive proportion of $χ$ (mod q) such that $L(χ, 1/2 ), L(χω_1, 1/2 )$ and $L(χω_2, 1/2)$ are simultaneously not too small.
Source: arXiv (Cornell University)
Author: Zacharias, Raphael
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2626820237