Period polynomials for Picard modular forms

Abstract

The relations satisfied by period polynomials associated to modular forms yield a way to count dimensions of spaces of cusp forms. After showing how these relations arise from those on the mapping class group $PSL(2,\mathbb{Z})$ of the moduli space ${\mathcal{M}}_{0,4}$ of genus 0 curves with 4 marked points, the author goes on to define period polynomials associated to Picard modular forms. Relations on these Picard period polynomials are then determined, and via an embedding of a monodromy representation of the moduli space ${\mathcal{M}}_{0,5}$ of genus 0 curves with 5 marked points in $PU(2,1;\mathbb{Z}[\rho ])$ (where $\rho$ denotes a third root of unity), they are related to the geometry of ${\mathcal{M}}_{0,5}.$

37 pages, 2 figures

References in corpus (1)

• Algebraic de Rham theory for weakly holomorphic modular forms of level one