A double-sum Kronecker-type identity

TL;DR

This paper proves a double-sum analog of a classical identity, expressing it through special functions and revealing its nature as a mixed mock modular form, along with related symmetric generalizations.

Contribution

It introduces a novel double-sum identity related to Kronecker's work and connects it to mixed mock modular forms and special functions.

Findings

Double-sum analog of Kronecker's identity proven

Expressed in terms of Appell and Lerch functions

Identified as a mixed mock modular form

Abstract

We prove a double-sum analog of an identity known to Kronecker and then express it in terms of functions studied by Appell and Kronecker's student Lerch, in so doing we show that the double-sum analog is of mixed mock modular form. We also give related symmetric generalizations.