On modular equations of degree 25
Tóm tắt
On page 237–238 of his second notebook, Ramanujan recorded five modular equations of composite degree 25. Berndt proved all these using the method of parametrization. He also expressed that his proofs undoubtedly often stray from the path followed by Ramanujan. The purpose of this paper is to give direct proofs to four of the five modular equations using the identities known to Ramanujan.
Tài liệu tham khảo
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Berndt, B.C.: Ramanujan Notebooks, Part III. Springer, New York (1991)
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Bhargava, S., Vasuki, K.R., Rajanna, K.R.: On some Ramanujan identities for the ratios of eta functions. Ukr. Math. J. 66(8), 1131–1151 (2015)
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