In this talk I would like to present some ideas behind a general Hilbert space framework for solving certain optimization problems that arise when studying the distribution of the low-lying zeros of families of L-functions. For instance, in connection to previous work of Iwaniec, Luo, and Sarnak (2000), we will discuss how to use information from one-level density theorems to estimate the proportion of non-vanishing of L-functions in a family at a low-lying height on the critical line. We will also discuss the problem of estimating the height of the first low-lying zero in a family, considered by Hughes and Rudnick (2003) and Bernard (2015). This is based on joint work with M. Milinovich and A. Chirre.
This video is part of the Number Theory Web Seminar series.
