Lambert series and double Lambert series

TL;DR

This paper explores the connections between classical Lambert series, multiple Lambert series, and Rogers-Ramanujan type q-series, and discusses the Andrews-Dixit-Schultz-Yee conjecture.

Contribution

It establishes relationships among various Lambert series and q-series, and provides insights into the conjecture by Andrews, Dixit, Schultz, and Yee.

Findings

Identified new relationships between Lambert series and q-series.

Provided analysis relevant to the Andrews-Dixit-Schultz-Yee conjecture.

Enhanced understanding of classical and multiple Lambert series connections.

Abstract

We consider relationships between classical Lambert series, multiple Lambert series and classical $q$-series of the Rogers-Ramanujan type. We conclude with a contemplation on the Andrews-Dixit-Schultz-Yee conjecture.