English

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}
}

Comments

15 pages, 0 figures, submitted

R2 v1 2026-07-01T12:02:13.325Z