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

Source abstract

We prove a Lindelöf-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 q2∣(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.