Searching for "moduli-friendly" automorphic forms

Zoom ID: 919 6497 4060.
For password please contact Pieter Moree (moree@mpim...).

One can systematically construct elliptic modular forms on $\Gamma(N)$ as Laurent coefficients of elliptic functions (on a varying elliptic curve) with prescribed zeros and poles at N-torsion points.  I will discuss this construction, as well as some of the issues that one encounters when one tries to generalize this setup to Siegel modular forms of higher degree.  Notably, meromorphic functions of several variables, such as elements of the function field of an abelian variety, almost never have Laurent expansions.  There are nonetheless some interesting leads worth pursuing.