# Traces of reciprocal singular moduli

## TL;DR

This paper demonstrates that the generating series of traces of reciprocal singular moduli forms a mixed mock modular form of weight 3/2, with its shadow expressed through theta functions, extending the Kudla-Millson theta lift to meromorphic functions.

## Contribution

It introduces a new connection between traces of reciprocal singular moduli and mixed mock modular forms, extending existing theta lift techniques to meromorphic functions.

## Key findings

- The generating series is a mixed mock modular form of weight 3/2.
- The shadow involves products of unary and binary theta functions.
- Extended Kudla-Millson theta lift to meromorphic modular functions.

## 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.