Title

The subconvexity problem for L-functions

Document Type

Conference Article

Publication Title

Proceedings of the International Congress of Mathematicians, ICM 2018

Abstract

Estimating the size of automorphic L-functions on the critical line is a centralproblem in analytic number theory. An easy consequence of the standard analyticproperties of the L-function is the convexity bound, whereas the generalised RiemannHypothesis predicts a much sharper bound. Breaking the convexity barrier is a hardproblem. The moment method has been used to surpass convexity in the case of Lfunctions of degree one and two. In this talk I will discuss a different method, whichhas been quite successful to settle certain longstanding open problems in the case ofdegree three.

First Page

381

Last Page

394

Publication Date

1-1-2018

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