Mathematics Department Colloquium
Thu, Dec 05
1:00 PM — 2:00 PM
NAC160 Convent Avenue
Karen Taylor (Bronx Community College), Fourier Coefficients of Hyperbolic Modular FormsIn the study of modular forms two constructions based on translation invariance arise: One is the fourier expansion of a modular form, the other is the Petersson Poincare series. In this talk we explore the analogous series based on invariance under a hyperbolic element of the modular group. This work initiated with Petersson (1941) who showed, in addition to the parabolic expansion, that modular forms have elliptic and hyperbolic expansions. We particularly highlight the algebra and geometry of real quadratic fields that arise in finding fourier coefficients of hyperbolic Eisenstein series. This is a preliminary report on joint work with Cormac O'Sullivan.