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, in his notation.
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