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arXiv · 1907.04852

Period polynomials for Picard modular forms

Sheldon Joyner
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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 $\mathcal{M}_{0,5}.$

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Sheldon Joyner. 2019-07-10. Period polynomials for Picard modular forms. https://arxiv.org/abs/1907.04852

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