Mollification of the fourth moment of Dirichlet $L$-functions
Volume 191 / 2019
Acta Arithmetica 191 (2019), 201-257
MSC: Primary 11M06; Secondary 11M26.
DOI: 10.4064/aa170901-16-10
Published online: 16 September 2019
Abstract
We evaluate some twisted fourth moment of Dirichlet $L$-functions at the central point $s={1/2}$ and for prime moduli $q$. The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using the spectral theory of automorphic forms. Having in mind simultaneous non-vanishing results, we apply our result to establish an asymptotic formula for a mollified fourth moment for this family of $L$-functions.
