Identities and transformations for Lambert series and double Lambert series
Number Theory
2026-04-13 v1
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.
Cite
@article{arxiv.2604.08839,
title = {Identities and transformations for Lambert series and double Lambert series},
author = {Su-Ping Cui and Dazhao Tang},
journal= {arXiv preprint arXiv:2604.08839},
year = {2026}
}
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