Videos

Murmurations and explicit formulas

Presenter
July 7, 2023
Abstract
We propose a heuristic explanation for murmurations based on the "explicit formula" from analytic number theory. A crucial ingredient in this heuristic is that the distribution of the zeros of the associated L-functions has a quasi-periodic structure. We present empirical results for both a family of elliptic curves as well as a family of quadratic Dirichlet characters that also exhibit murmurations.