Zeros of L-functions have been extensively studied, due to their close connection to arithmetic problems. Despite several precise conjectures about their behaviour, our unconditional understanding of them remains limited. In this talk we will discuss certain intrinsic properties of such zeros, focusing on what is known (in degrees 1 and 2) about their accumulation on the central line and their multiplicity. Here the tools of analytic number theory can give quantitative advances, and we will show how to deduce that there are many zeros of multiplicity one for the L-function associated to a modular form.
This video is part of the Institute for Advanced Study‘s Members’ colloquium.
