Traces of reciprocal singular moduli

Abstract

We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight $3/2$ whose shadow is given by a linear combination of products of unary and binary theta functions. To prove these results, we extend the Kudla-Millson theta lift of Bruinier and Funke to meromorphic modular functions.

References in corpus (5)

• Automorphic forms with singularities on Grassmannians
• On a theta lift related to the Shintani lift
• CM values of regularized theta lifts and harmonic weak Maaß forms of weight one
• On the rationality of cycle integrals of meromorphic modular forms
• Squashed Toric Manifolds and Higher Depth Mock Modular Forms