Holomorphic projection for sesquiharmonic Maass forms

TL;DR

This paper investigates the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms, providing explicit expressions and analyzing related L-series and convolution sums.

Contribution

It introduces new methods for holomorphic projection of sesquiharmonic Maass forms and expresses complex functions in terms of eta quotients.

Findings

Explicit expression for holomorphic projection involving class numbers and theta functions

Analysis and bounds for shifted convolution L-series

Numerical expressions for special cases

Abstract

We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a certain theta function in terms of eta quotients. We also analyze certain shifted convolution $L$-series involving mock modular forms and bound certain shifted convolution sums.