The authors prove an identity generalizing the Amdeberhan-Andrews-Ballantine conjecture on double Lambert series using coefficients from the generalized divisor function σ_k(n).
Transformation Formulae and Applications for Double Lambert Series
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abstract
In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing certain double Lambert series to single Lambert series. As applications, we derive identities related to recent conjectures of Andrews, Dixit, Schultz, and Yee, and of Amdeberhan, Andrews, and Ballantine. We also propose a new proof of a result of Amdeberhan, Andrews, and Ballantine.
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2026 1verdicts
UNVERDICTED 1representative citing papers
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A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
The authors prove an identity generalizing the Amdeberhan-Andrews-Ballantine conjecture on double Lambert series using coefficients from the generalized divisor function σ_k(n).