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ON SOME P-Q MIXED MODULAR EQUATIONS OF DEGREE 5

M. S. MAHADEVA NAIKA|S. Chandankumar|M. Harish
장전수학회 (Jangjeon Mathematical Society)|2020.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제23권 제3호|pp. 305-319|DOI 10.17777/pjms.2020.23.3.003

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참고문헌

키워드

Modular equationsTheta-functionsRemarkable product of theta-functions
주제분류수학

초록

In his second notebook, Ramanujan recorded total of 23 P-Q modular equations in- volving theta-functions ρ(q), Ψ(q) and f(-q). In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving f(-q). As a consequence, several values of quotients of theta-function are evaluated.

Abstract

In his second notebook, Ramanujan recorded total of 23 P-Q modular equations in- volving theta-functions ρ(q), Ψ(q) and f(-q). In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving f(-q). As a consequence, several values of quotients of theta-function are evaluated.

참고문헌 (14)

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  2. N. D. Baruah, "Two parameters for Ramanujan's theta-functions and their explicit values", Rocky Mountain J. Math, 37(6), pp.1747~1790 (2007)
  3. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  4. B. C. Berndt, "Ramanujan's Notebooks, Part IV" (1994), Springer-Verlag
  5. B. C. Berndt, "Ramanujan's identities for eta-functions", Math. Ann, 292(1), pp.561~573 (1992)
  6. B. C. Berndt, "A new class of theta-function identities originating in Ramanujan's notebooks", J. number theory, 48(2), pp.224~242 (1994)
  7. S. Bhargava, "A new class of modular equations in Ramanujan's alternative theory of elliptic function of signature 4 and some new P-Q eta-function identities", Indian J. Math, 45(1), pp.23~39 (2003)
  8. M. S. Mahadeva Naika, "New modular relations for Ramanujan's parameter", Int. J. Pure Appl. Math, 74(4), pp.413~435 (2012)
  9. M. S. Mahadeva Naika, "On some remarkable product of theta-function", Aust. J. Math. Anal. Appl, 5(1), pp.1~15 (2008)
  10. M. S. Mahadeva Naika, "On some new P-Q mixed modular equations", Ann. Univ. Ferrara Sez. VII (N.S.), 59(2), pp.353~374 (2013)
  11. M. S. MAHADEVA NAIKA, "ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONS", Advanced Studies in Contemporary Mathematics, 23(3), pp.431~448 (2013), 장전수학회
  12. M. S. Mahadeva Naika, "On some new Modular relations for a re-markable product of theta-functions", Tbil. Math. J, 7(1), pp.55~68 (2014)
  13. S. Ramanujan, "Notebooks (2 volumes)" (1957), Tata Institute of Fundamental Research
  14. S. Ramanujan, "The lost notebook and other unpublished papers" (1988), Narosa

관련 논문AI추천

CERTAIN 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 Schläfli type mixed modular equationsK. S. Bairy, M. S. M. Naika장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호ON 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 modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호A NOTE ON SCHLÄFLI TYPE MODULAR EQUATIONS OF COMPOSITE DEGREESMohandas장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제4호A 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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