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New Modular Relations for the Ratio’s of Ramanujan Function χ(−q) of degree 9
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In this paper, we establish some new modular equations of Ramanujan’s function χ(−q) of degree 9. Further, we obtain some explicit evaluations of class invariant gn from them.
Abstract
In this paper, we establish some new modular equations of Ramanujan’s function χ(−q) of degree 9. Further, we obtain some explicit evaluations of class invariant gn from them.
참고문헌 (8)
- B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan’s Notebooks, Part IV" (1994), Springer-Verlag
- M. S. Mahadeva Naika, "Modular equations for the ratios of Ramanujan’s theta function and evaluations", New Zealand J. Math, 40(1), pp.33~48 (2010)
- N. D. Baruah, "Two parameters for Ramanujan’s theta-functions and their explicit values", Rocky Mountain J.Math, 36(6), pp.1747~1790 (2007)
- Nipen Saikia, "Ramanujans modular equations and Weber-Ramanujan class invariants Gn and gn", Bull. Math. Sci, 2, pp.205~223 (2012)
- S. -Y. Kang, "Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan’s lost notebook", Ramanujan J, 3(1), pp.91~11 (1999)
- Notebooks (2 volumes). Bombay, "S. Ramanujan", Tata Institute of Fundamental Research, ~ (1957)
- The ‘lost’ notebook and other unpublished papers, "S. Ramanujan", ~ (1988)
관련 논문AI추천
On some new modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호Further evaluations of Ramanujan-Weber class invariants $g_n$B. R. Rakshith, G. N. Rajappa, Veeresha R.G.장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제1호Further evaluations of Ramanujan-Weber class invariants g_nB. R. Rakshith, G. N. Rajappa, R. G. veeresha장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제3호On Some Modular Equations in the Spirit of RamanujanBelakavadi Radhakrishna Srivatsa Kumar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호On certain Ramanujan's modular equations of degree 7K. R. Vasuki, R. G. veeresha장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제1호New identities for ratios of Ramanujan’s theta functionK. Sushan Bairy, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호
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