Seminar in Algebraic Geometry and Number Theory

Abstract: In this talk, I will introduce a scalar-valued Eichler-Shimura integral of depth two, and show that it is a component of a vector-valued modular form of a certain extension type. I will also show that the existence of this extension type provides an alternative proof of an orthogonality relation satisfied by period polynomials that is originally due to Pasol and Popa. I will emphasize throughout the relation of this research to existing research on higher order modular forms, Eichler cohomology, and iterated Eichler-Shimura integrals.

The talk is based on joint work with Martin Raum, and in particular the paper "Scalar-valued depth two Eichler-Shimura Integrals of Cusp Forms" (arXiv:2209.00488).