A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture

Rong Chen; Tianjian Xu

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arXiv · 2606.06086

A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture

Rong Chen·Tianjian Xu

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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 $\sigma_k(n)$. As a special case, our result includes the original conjecture.

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Rong Chen, Tianjian Xu. 2026-06-04. A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture. https://arxiv.org/abs/2606.06086

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