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On two interesting Somos’s theta function identities of level 14. (English) Zbl 07828501

Summary: Michael Somos has discovered around 6300 theta function identities using computer and runs PARI/GP scripts. In this paper, we give a proof of two Somos’s interesting and elegant theta function identities of level 14 and also we derive two \(P\)-\(Q\) theta function identities of level 14 due to Ramanujan.

MSC:

11F11 Holomorphic modular forms of integral weight
11F20 Dedekind eta function, Dedekind sums
Full Text: DOI

References:

[1] Berndt B. C., Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991. · Zbl 0733.11001
[2] Berndt B. C., Ramanujan’s Notebooks, Part IV, Springer-Verlag, New York, 1994. · Zbl 0785.11001
[3] Ramanujan S., The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. · Zbl 0639.01023
[4] Vasuki K. R., On Some Ramanujan’s Schläfli Type Modular Equations, Aus. J. Math. Anal. Appl., 3(2) (2006), 1-8. · Zbl 1167.33314
[5] Vasuki K. R. and Srivatsa Kumar B. R., Certain Identities for Ramanujan-Göllnitz-Gordon Continued Fraction, J. Comp. Appl. Math., 187 (2006), · Zbl 1081.11004
[6] Vasuki K. R. and Veeresha R. G., On Somos’s theta-function identities of level 14, Ramanujan J., 42 (2017), 131-144. · Zbl 1412.11070
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