Connections between the circle method, trace formula and bounds for the subconvexity problem.

Abstract: After introducing the sub-convexity problem for L-functions in a general context, we will focus our attention to the particular case of Rankin-Selberg L-functions. We will briefly trace the history of this particular problem starting from Kowalski, Michel, and Vanderkam, with a lot of authors in between upto the seminal work of Michel, Venkatesh. I will then try to explain how the circle method enters this question by sketching an argument of Munshi for what is perhaps the simplest case i.e character twists of GL(2) L-functions. I will end the talk by explaining how we can solve the Subconvexity problem for Rankin-Selberg L-functions in the combined level aspect by a very easy version of the circle method and see how this approach is connected to earlier work on the same problem.

number theory

Audience: researchers in the topic

CMI seminar series

Series comments: Please visit the seminar series homepage for streaming details. Timings of the seminar vary from week to week.