Differential bimodular forms with given residues

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

This  talk will be about the construction of the modular forms in two variables, which are the representatives of the smooth cohomology classes of the modular surfaces. Namely, it will be considered the case of the complement to the Hecke curve (the graph of a Hecke correspondence) on the product of two standard modular curves  $Y_0(1)^2$. Explicit expressions for the smooth representatives of the cohomology classes are effective for solving various problems. For example, a smooth representative of a correspondence class allows to describe the action of this correspondence on cohomology in terms of an integral operator. The second part of this  talk will be devoted to the study of such differential forms in the case of the Hilbert modular surface