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arXiv · 1908.10346

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

Ian Petrow·Matthew P. Young
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Abstract

We prove a Lindel\"of-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.

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BibTeXRIS

Ian Petrow, Matthew P. Young. 2019-08-27. The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound. https://doi.org/10.1215/00127094-2022-0069

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