Second Moment of GL(3) L-functions

Understanding the critical values of L-functions is a fundamental problem in number theory. In this talk, I will discuss recent joint work with Agniva Dasgupta and Matthew Young on the second moment of the standard GL(3) L-functions on the critical line. We establish a non-trivial upper bound for this second moment, leading to several interesting applications, including an improvement on the classical Rankin–Selberg problem. The proof relies on a delicate interplay between the delta method and the large sieve inequality.