Bounds for standard L-functions

Time:Tues.,15:30-16:30pm, Dec.13,2022

Venue:Zoom ID: 293 812 9202 ;PW: BIMSA

Organizer:Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu

Speaker:Paul Nelson (Aarhus University)


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.


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.


DATEDecember 13, 2022
Related News
    • 0

      New Ramsey multiplicity bounds and search heuristics

      AbstractWe study two related problems concerning the number of monochromatic cliques in two-colorings of the complete graph that go back to questions of Erdős. Most notably, we “significantly” improve the best known upper bounds on the Ramsey multiplicity of K_4 and K_5 and settle the minimum number of independent sets of size four in graphs with clique number at most four. Motivated by the ...

    • 1

      Differential Geometry Seminar | Spectral bounds on hyperbolic 3-manifolds

      Abstract:I will discuss some new bounds on the spectra of Laplacian operators on hyperbolic 3-manifolds. One example of such a bound is that the spectral gap of the Laplace-Beltrami operator on a closed orientable hyperbolic 3-manifold must be less than 47.32, or less than 31.57 if the first Betti number is positive. The bounds are derived using two approaches, both of which employ linear prog...