A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture

Abstract

In this paper, we prove a generalization of a conjecture of Amdeberhan, Andrews, and Ballantine on double Lambert series. Motivated by a question raised by Cui, Kumar, and Singh concerning the existence of a generalization of this conjecture, we establish an identity in which the coefficients are given by the generalized divisor function $σ_k(n)$. As a special case, our result includes the original conjecture.