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Number Theory Seminar

Infinitely many zeros of L-functions on the critical line, and an algebraic-geometric proof of multiplicity one for Whittaker functions

Doyon Kim, Rutgers University

Location:  Zoom
Date & time: Tuesday, 26 October 2021 at 2:30PM - 3:30PM

Abstract: In this talk, I will present two applications of automorphic distributions. The first is on infinitely many zeros of L-functions on the critical line with a result on L-functions with additive twists, and the second is on proving the existence and uniqueness of Whittaker functions on GL(n,R).

The first problem uses a variant of Hardy-Littlewood method. Representing an L-function as integral of the corresponding automorphic distribution instead of automorphic form makes the integral much easier to bound. The second problem concerns the algebraic geometry of Schubert cells for GL(n,R). Once we establish the existence of certain birational map for each Schubert cell, a proof of the existence and uniqueness of Whittaker functions can be deduced. I will describe the combinatorics of such birational maps and discuss my ongoing work on proving it.

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