The fourth moment of Dirichlet L-functions along a coset and the Weyl bound

By Ian Petrow, M. Young. Duke mathematical journal, 2019

62 citations recorded by the source corpus.

We prove a Lindelof-on-average upper bound for the fourth moment of Dirichlet $L$-functions of conductor $q$ along a coset of the subgroup of characters modulo $d$ when $q^*|d$, where $q^*$ is the least positive integer such that $q^2|(q^*)^3$. As a consequence, we finish the previous work of the authors and establish a Weyl-strength subconvex bound for all Dirichlet $L$-functions with no restrictions on the conductor.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/150eab9d0ace87c7d8101b854eae47be77e114f7