Agniva Dasgupta, University of Texas at Dallas
Second Moment of GL(3) L-functions
In this talk, I will discuss our recent result, joint with Wing Hong Leung and Matthew Young, on the second moment of GL(3) L-functions on the critical line. Moments of L-functions on the critical line have been studied for over a hundred years now, and still remains a very active field of research in number theory. The second moment of GL(3) L-functions has proved to be especially difficult, and only in the last couple of years have we seen some progress on this. Building on top of these works, we are able to obtain a strong upper bound for this moment. This allows us to deduce some nice corollaries including an improvement on the error term in the Rankin-Selberg problem, and on certain subconvexity bounds for GL(3) x GL(2) and GL(3) L-functions. As a byproduct of the method of proof, we also obtain an improved estimate for an average of shifted convolution sums of GL(3) Fourier coefficients.
MC 5479