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arXiv · 2604.08839

Identities and transformations for Lambert series and double Lambert series

Su-Ping Cui·Dazhao Tang
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Abstract

We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andrews and Ballantine (J Combin Theory Series A 221:106154, 2026). The proofs are based on classical transformations in the theory of infinite series together with a systematic rearrangement of double Lambert series.

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Su-Ping Cui, Dazhao Tang. 2026-04-10. Identities and transformations for Lambert series and double Lambert series. https://arxiv.org/abs/2604.08839

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