Algebra Seminar: Martin Raum | Department of Mathematics

Algebra Seminar: Martin Raum

Event Information
Event Location: 
ZOOM
Event Date: 
Friday, April 23, 2021 - 1:00pm

Title: An alternative way to compute modular forms

Abstract: There are two established exact methods to compute Fourier expansions modular forms: Via modular symbols and via trace formulas. Due to their tight connection to cohomology of groups and modular varieties, they inherit some of the common limitations. In particular, general cusp expansions and vector-valued notions of modular forms are impossible to access through them. This opens a niche for one further type of algorithm, which covers these aspects.

We discuss how the Rankin-Selberg convolution provides a whole class of algorithms which deliver Fourier expansions of modular forms including their cusp expansions. An implementation of the case of elliptic modular forms reveals an shift away from usual performance issues with around linear algebra to more group and representation theoretic concerns.