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On some new Schläfli type mixed modular equations

M. S. M. Naika|K. S. Bairy
장전수학회 (Jangjeon Mathematical Society)|2011.04|Advanced Studies in Contemporary Mathematics|제21권 제2호|pp. 189-206

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Modular equationClass invariantTheta-function
주제분류수학

초록

On pages 86 and 88 of his rst notebook, Ramanujan recorded eleven Schla i-type modular equations for composite degrees. Out of eleven, ten have been proved by Berndt [5] using theory of modular forms. In this paper, we establish several new Schla i-type mixed modular equations.

Abstract

On pages 86 and 88 of his rst notebook, Ramanujan recorded eleven Schla i-type modular equations for composite degrees. Out of eleven, ten have been proved by Berndt [5] using theory of modular forms. In this paper, we establish several new Schla i-type mixed modular equations.

참고문헌 (17)

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  5. B.C.Berndt, "Ramanujan's Notebooks, Part V" (1998), Springer-Verlag
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  8. M. S. Mahadeva Naika, "P-Q eta-function identities and computation of Ramanujan-Weber class invariants", J. Indian Math. Soc, 70(1), pp.121~134 (2003)
  9. M. S. MAHADEVA NAIKA, "SOME NEW EXPLICIT VALUES FOR RAMANUJAN CLASS INVARIANTS", Advanced Studies in Contemporary Mathematics, 20(4), pp.557~567 (2010), 장전수학회
  10. M.S. Mahadeva Naika, "Certain quotient of eta-function identities", Advanced Studies in Contemporary Mathematics, 16(1), pp.121~136 (2008), 장전수학회
  11. M. S. Mahadeva Naika, "On some new explicit evaluations of class invariants", Vietnam J. Math, 36(1), pp.103~124 (2008)
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  14. G. N. Watson, "Some Singular moduli(II)", Quart. J. Math, 3, pp.189~212 (1932)
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  17. E.T.Whittaker, "A Course of Modern Analysis, 4th ed" (1966), Cambridge University Press

관련 논문AI추천

A NOTE ON SCHLÄFLI TYPE MODULAR EQUATIONS OF COMPOSITE DEGREESMohandas장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제4호ON SOME P-Q MIXED MODULAR EQUATIONS OF DEGREE 5M. Harish, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호CERTAIN MODULAR RELATIONS FOR REMARKABLE PRODUCT OF THETA-FUNCTIONSK. Sushan Bairy, M. S. MAHADEVA NAIKA, N. P. SUMAN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제3호On Some Modular Equations in the Spirit of RamanujanBelakavadi Radhakrishna Srivatsa Kumar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONSB. HEMANTHKUMAR, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호ON SOME NEW SCHLAFLI􀀀TYPE CUBIC MODULAR EQUATIONS김영희, 김태균, 이병제, 장이채, Kumar, Naika장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호

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