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Further evaluations of Ramanujan-Weber class invariants g_n

B. R. Rakshith|R. G. veeresha|G. N. Rajappa
장전수학회 (Jangjeon Mathematical Society)|2012.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제15권 제3호|pp. 241-258|DOI 10.17777/pjms.2012.15.3.002

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키워드

Eta function identitiesClass invariants
주제분류수학

초록

The purpose of this paper is to establish further evaluations of the class invariants gn using Ramanujan's modular equations.

Abstract

The purpose of this paper is to establish further evaluations of the class invariants gn using Ramanujan's modular equations.

참고문헌 (17)

  1. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  2. B. C. Berndt, "Ramanujan and the J-invariant", Canad. Math. Bull., 42, pp.427~440 (1999)
  3. B. C. Berndt, "Ramanujan's class invariants and cubic continued fraction", Acta Arith., 72, pp.67~85 (1995)
  4. B. C. Berndt, "Ramanujan's singular moduli", The Ramanujan J., 1, pp.53~74 (1997)
  5. B. C. Berndt, "Ramanujan's class invariants with applications to the values of q-continued fractions and theta func- tions, in: Special Function, In Fields Institute Communication Series, 14", pp.37~53 (1997), AMS Providence
  6. B. J. Birch, "Weber's class invariants", Mathematika, 16, pp.283~294 (1969)
  7. S. Bhargava, "Evaluations of Ramanujan-Weber class invariants gn", J. Indian Math. Soc., 72(1), pp.115~127 (2005)
  8. H. H. Chan, "Ramanujan's Weber class invariants Gn and Watson's empirical process", J. Londan Math. Soc., 57, pp.545~561 (1998)
  9. D. A. Cox, "Primes of the form x2 + ny2" (1987), Wiley New York
  10. E. Konstantinou, , Computers and Mathematics with Applications, 59, pp.2901~2917 (2010)
  11. S. Lang, "Elliptic Functions, 2nd ed." (1987), Springer
  12. S. Ramanujan, "Modular equations and approximations to", Quart. J. Math. (Oxford), 45, pp.350~372 (1914)
  13. S. Ramanujan, "Notebooks (2 volumes)" (1957), Tata Institute of Fundamental Research
  14. S. Ramanujan, "The lost notebook and other unpublished paper" (1988), Narosa
  15. G. N. Watson, "Some singular moduli (I)", Quart. J. Math., 3, pp.81~98 (1932)
  16. G. N. Watson, "Some singular moduli (II)", Quart. J. Math., 3, pp.189~212 (1932)
  17. H. Weber, "Lehrbuch der Algebra, III, 2nd ed., Braunschweig, (1908)" (1961), Chelsea

관련 논문AI추천

Further evaluations of Ramanujan-Weber class invariants $g_n$B. R. Rakshith, G. N. Rajappa, Veeresha R.G.장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제1호On 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 Modular Relations for the Ratio’s of Ramanujan Function χ(−q) of degree 9B. N. DHARMENDRA, P. S. Guruprasad장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호A note on modular equations of signature 2 and their evaluationsArjun Kumar Rathie, Belakavadi Radhakrishna Srivatsa Kumar, Nagara Vinayaka Udupa Sayinath, SHRUTHI대한수학회 · 대한수학회논문집2022 · 제37권 제1호On evaluations of the modular $j$--invariant by modular equations of degree 2Dae Hyun Paek, Jinhee Yi대한수학회 · 대한수학회보2015 · 제52권 제1호

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