English

Cubic and quintic analogues of Ramanujan's septic theta function identity

Number Theory 2025-06-03 v2 Classical Analysis and ODEs

Abstract

On page 206 in his lost notebook, Ramanujan recorded an incomplete septic theta function identity. Motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. Using the theory generated by these two analogues and Ramanujan's class invariants, we provide many evaluations for Ramanujan's most prominent theta function, φ(q)\varphi(q) in his notation.

Keywords

Cite

@article{arxiv.2312.15513,
  title  = {Cubic and quintic analogues of Ramanujan's septic theta function identity},
  author = {Bruce C. Berndt and Örs Rebák},
  journal= {arXiv preprint arXiv:2312.15513},
  year   = {2025}
}

Comments

33 pages, submitted