English

Ninth degree analogue of Ramanujan's septic theta function identity

Number Theory 2025-06-03 v1 Classical Analysis and ODEs

Abstract

On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function φ(q)\varphi(q). We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for φ(eπn)\varphi(e^{-\pi\sqrt{n}}).

Keywords

Cite

@article{arxiv.2506.01181,
  title  = {Ninth degree analogue of Ramanujan's septic theta function identity},
  author = {Sun Kim and Örs Rebák},
  journal= {arXiv preprint arXiv:2506.01181},
  year   = {2025}
}

Comments

21 pages, submitted