Bounds for standard L-functions

Abstract

We consider the standard L-function attached to a cuspidal automorphic representation of a general linear group. We present a proof of a subconvex bound in the t-aspect. More generally, we address the spectral aspect in the case of uniform parameter growth. These results are the subject of the third paper linked below, building on the first two.

Speaker

Paul Nelson works in Analytic Number Theory and Representation Theory of Automorphic Forms. An important problem to which he has made spectacular contributions is the so-called subconvexity problem for L-functions. L-functions are meromorphic functions that encode important arithmetic information, and the subconvexity problem is about estimating their values on the critical line Re(s) = 1/2. The strongest possible form of subconvexity is known as the Lindelöf Hypothesis, an extremely difficult open problem lying very close to the famous Riemann Hypothesis, one of the Clay Millennium Problems. Paul Nelson has made strong improvements to the subconvexity problem by obtaining the first subconvexity bounds ever for a large class of L-functions.

Paul Nelson obtained his BA from Princeton in 2006, followed by a PhD from Caltech under the supervision of Dinakar Ramakrishnan obtained in 2011. He subsequently moved to École Polytechnique Fédérale de Lausanne in Switzerland for a three-year postdoctoral position, followed by an appointment as assistant professor at ETH Zürich. Just prior to joining the Department of Mathematics in Aarhus, he was a member of the Institute for Advanced Study in Princeton.

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https://math.au.dk/en/currently/news/news-item/artikel/paul-nelson-new-associate-professor-in-mathematics