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arXiv · 2312.15513

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

Bruce C. Berndt·Örs Rebák
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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, $\varphi(q)$ in his notation.

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Bruce C. Berndt, Örs Rebák. 2023-12-24. Cubic and quintic analogues of Ramanujan's septic theta function identity. https://doi.org/10.1007/s11139-024-01013-2

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