Poincar\'e square series of small weight
Brandon Williams
TL;DR
This paper extends previous work by providing explicit coefficient formulas for quasimodular Poincaré square series of weights 3/2 and 2 related to the dual Weil representation of an even lattice.
Contribution
It introduces new explicit formulas for Poincaré square series coefficients in weights 3/2 and 2, expanding the understanding of their structure.
Findings
Derived explicit coefficient formulas for weight 3/2 series
Derived explicit coefficient formulas for weight 2 series
Enhanced computational tools for quasimodular Poincaré series
Abstract
We extend the author's earlier computation and give coefficient formulas for the (quasimodular) Poincar\'e square series of weight 3/2 and weight 2 for the dual Weil representation for an even lattice.
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