University of Arizona
When
2 – 3 p.m., Oct. 29, 2024
Where
Title: Mod-p modular forms: explicit Galois representations and applications to densities
Abstract: We tell the story of mod-p modular forms, focusing on the example of p = 2 and p = 3 and level 1: the Hecke algebra acting on the space of forms, the Galois representation carried thereby, and explicit matrix realization thereof. An application is studying the *density* of a mod-p modular form, which captures the distribution of its prime Fourier coefficients. The p = 2 case relies on published and unpublished work of Bellaïche, Nicolas, and Serre.