The Weyl bound for Dirichlet $L$-functions

Abstract: The problem of bounding $L$-functions has a long history. For the Riemann zeta function, the method of Weyl gives a subconvexity bound with exponent $1/6$, which is now called the Weyl bound. Many questions on the zeta function in the t-aspect have a natural analog for Dirichlet $L$-functions in the q-aspect, but the latter is in general much harder. Indeed, the first subconvexity result for Dirichlet $L$-functions, due to Burgess in the 1960's, has a weaker exponent $3/16$. In this talk I will discuss work with Ian Petrow that proves the Weyl bound for all Dirichlet $L$-functions.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

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