논문KCI 등재
A NOTE ON SCHLÄFLI TYPE MODULAR EQUATIONS OF COMPOSITE DEGREES
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초록
S. Ramanujan documented certain modular equations in his recordings and many mathematicians employed them for the explicit calculation of theta functions, Weber-class invariants, Continueed fractions and many more. Motivated by their work, in this paper, we found few modular equations of the similar type.
Abstract
S. Ramanujan documented certain modular equations in his recordings and many mathematicians employed them for the explicit calculation of theta functions, Weber-class invariants, Continueed fractions and many more. Motivated by their work, in this paper, we found few modular equations of the similar type.
참고문헌 (12)
- C. Adiga, "On Ramanujan’s cubic continued fraction and explicit evaluations of theta-functions", Indian J. Pure Appl. Math, 35(9), pp.1047~1062 (2004)
- N. D. Baruah, "Modular equations for Ramanujan’s cubic continued fraction", J. Math. Anal. Appl, 268(1), pp.244~255 (2002)
- N. D. Baruah, "On some of Ramanujan’s Schlafli-type mixed modular equations", J. Number Theory, 100(2), pp.270~294 (2003)
- B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer
- B. C. Berndt, "Ramanujan’s Notebooks, Part IV" (1996), Springer
- M. S. M. Naika, "Modular equations for the ratios of Ramanujan’s theta function and evaluations", New zealand Journal of Mathematics, 40, pp.33~48 (2010)
- S. Ramanujan, "Notebooks (2 Volumes)" (1957), Tata Institute of Fundamental Research
- K. R. Vasuki, "A note on P-Q modular equations", Tamsui Oxf. J. Math. Sci, 21(2), pp.109~120 (2005)
- K. R. Vasuki, "Evaluation of the Ramunujan-Gollnitz-Gordon continueed fraction H(q)by modular equations", Indian J. Mathematics, 48, pp.275~300 (2006)
- J. Yi, "Theta-function identities and the explicit formulas for theta-function and their applications", J. Math. Anal. Appl, 292, pp.381~400 (2004)
- B. R. Srivatsa Kumar, "Shruthi, A note on modular equations of signature 2 and their evaluations", Communications of the Korean Mathematical Society, 37(1), pp.31~43 (2022)[DOI]
- Saikia, N., "Some new modular equations in Ramanujan’s alternate theory of signature 3", Ramanujan J, 50, pp.163~194 (2019)[DOI]
관련 논문AI추천
On some new Schläfli type mixed modular equationsK. S. Bairy, M. S. M. Naika장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호A note on modular equations of signature 2 and their evaluationsArjun Kumar Rathie, Belakavadi Radhakrishna Srivatsa Kumar, Nagara Vinayaka Udupa Sayinath, SHRUTHI대한수학회 · 대한수학회논문집2022 · 제37권 제1호ON 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 제3호ON SOME NEW SCHLAFLITYPE CUBIC MODULAR EQUATIONS김영희, 김태균, 이병제, 장이채, Kumar, Naika장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호CERTAIN 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 new modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호
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