Washington State
University
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
Meet on Zoom
https://wsu.zoom.us/j/99273222985?pwd=T3ZNR2cxZDZTWndzd2taRTZzNk5QUT09
Meeting ID: 992 7322 2985
Password: M410
February 13, Monday, 4:10 - 5:00 PM
Peter Humphries
Department of Mathematics
University of Virginia
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
Meet on Zoom
https://wsu.zoom.us/j/99273222985?pwd=T3ZNR2cxZDZTWndzd2taRTZzNk5QUT09
Meeting ID: 992 7322 2985
Password: M410
February 13, Monday, 4:10 - 5:00 PM
Peter Humphries
Department of Mathematics
University of Virginia
Title: Hybrid subconvex bounds for self-dual GL(3)
L-functions via spectral reciprocity
Abstract: We discuss the subconvexity problem in the setting of GL(3) x GL(2) x GL(1) Rankin-Selberg L-functions involving a fixed GL(3) automorphic form, a GL(2) automorphic form, and a twist by a primitive Dirichlet character. In favourable situations, namely when the GL(3) form is self-dual, the central value of this L-function is non-negative. In this setting, we show how one can obtain subconvex bounds for this central L-value in the GL(2)- and GL(1)-aspects by extending a first moment method pioneered by Conrey and Iwaniec and later by Xiaoqing Li. We reformulate their approaches in the language of spectral reciprocity: exact identities for moments of L-functions in terms of other moments of L-functions. This is joint work with Soumendra Ganguly, Yongxiao Lin, and Ramon Nunes.
Abstract: We discuss the subconvexity problem in the setting of GL(3) x GL(2) x GL(1) Rankin-Selberg L-functions involving a fixed GL(3) automorphic form, a GL(2) automorphic form, and a twist by a primitive Dirichlet character. In favourable situations, namely when the GL(3) form is self-dual, the central value of this L-function is non-negative. In this setting, we show how one can obtain subconvex bounds for this central L-value in the GL(2)- and GL(1)-aspects by extending a first moment method pioneered by Conrey and Iwaniec and later by Xiaoqing Li. We reformulate their approaches in the language of spectral reciprocity: exact identities for moments of L-functions in terms of other moments of L-functions. This is joint work with Soumendra Ganguly, Yongxiao Lin, and Ramon Nunes.