Videos

Murmurations of Dirichlet Characters

Presenter
July 6, 2023
Abstract
Although murmurations were originally observed in the context of elliptic curves, it was soon discovered that this phenomenon occurred in other arithmetic contexts. Recent work with He, Lee, Oliver, and Sutherland showed that one can observe murmurations in many different families of L-functions. Simultaneously, Zubrilina provided a much needed theoretical explanation for murmurations by computing a local average over weight 2 modular newforms coming from all Galois orbit sizes. In my talk, I will provide a similar theoretical explanation in the context of degree 1 L-functions. In particular, I will compute a local average over Dirichlet characters of a fixed parity coming from all Galois orbit sizes, allowing us to predict the corresponding murmuration. This is based on recent work with Lee and Oliver.