Integrality of regularized Petersson inner product

Abstract: Petersson inner products of classical cusp forms contain important arithmetic information, such as congruences of modular forms. When the cusp forms are replaced by meromorphic modular form, the Petersson inner product can still be defined and calculated after suitable regularization. It turns out these regularized inner product also carry interesting arithmetic information, such as special values of derivatives of L-function. In this talk, we will recall some of these results, and discuss a joint work with Markus Schwagenscheidt from ETH, where we obtained an integrality result of such regularized inner products involving unary theta functions.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar