Olav Richter

Affiliation: University of North Texas

Title Of Talk: Weighted recursions for Hurwitz class numbers

Abstract: I will report on recent joint work with Matthew Ortiz and Martin Raum. We establish new recursions for Hurwitz class numbers with polynomial weights. In contrast to previous recursions, our results decouple class numbers of even and odd discriminants. Our main tool is the vector-valued holomorphic projection operator applied to mock modular forms. We invoke representation theory to connect the relevant spaces of vector-valued modular forms to spaces of classical new and old forms. We thereby leverage the vanishing of spaces of vector-valued cusp forms not available in the scalar case.

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