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 . 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 .
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