논문KCI 등재
CERTAIN MODULAR RELATIONS FOR REMARKABLE PRODUCT OF THETA-FUNCTIONS
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초록
At scattered places of his second notebook, Ramanujan recorded several P Q mixed modular equations with four moduli. In this paper, we establish several new P Q mixed modular equations analogous to those recorded by Ramanujan in his notebooks. Employing these, we establish new modular relations for Ramanujan's remarkable product of theta-functions.
Abstract
At scattered places of his second notebook, Ramanujan recorded several P Q mixed modular equations with four moduli. In this paper, we establish several new P Q mixed modular equations analogous to those recorded by Ramanujan in his notebooks. Employing these, we establish new modular relations for Ramanujan's remarkable product of theta-functions.
참고문헌 (5)
- C. Adiga, "Modular equations in the theory of signature 3 and P - Q identities", Adv. Stud. Contemp. Math, 7(1), pp.33~40 (2003)
- 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)
- B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan's Notebooks, Part IV" (1994), Springer-Verlag
- B. C. Berndt, "Ramanujan's remarkable product of the theta-function", Proc. Edin-burgh Math. Soc, 40, pp.583~612 (1997)
관련 논문AI추천
ON 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 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 modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호On some new Schläfli type mixed modular equationsK. S. Bairy, M. S. M. Naika장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호New identities for ratios of Ramanujan’s theta functionK. Sushan Bairy, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호A note on modular equations of signature 2 and their evaluationsArjun Kumar Rathie, Belakavadi Radhakrishna Srivatsa Kumar, Nagara Vinayaka Udupa Sayinath, SHRUTHI대한수학회 · 대한수학회논문집2022 · 제37권 제1호
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