과제정보
This study was financially supported by NRF 2021R1F1A1055200.
참고문헌
- N. D. Baruah and N. Saikia, Some general theorems on the explicit evaluations of Ramanujan's cubic continued fraction, J. Comput. Appl. Math. 160 (2003), no. 1-2, 37-51. https://doi.org/10.1016/S0377-0427(03)00612-5
- B. Cho, J. K. Koo, and Y. K. Park, Arithmetic of the Ramanujan-Gollnitz-Gordon continued fraction, J. Number Theory 129 (2009), no. 4, 922-947. https://doi.org/10.1016/j.jnt.2008.09.018
- B. Cho, J. K. Koo, and Y. K. Park, On Ramanujan's cubic continued fraction as a modular function, Tohoku Math. J. (2) 62 (2010), no. 4, 579-603. https://doi.org/10.2748/tmj/1294170348
- S. Cooper, Ramanujan's Theta Functions, Springer, 2017.
- W. D. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 2, 137-162. https://doi.org/10.1090/S0273-0979-05-01047-5
- N. Ishida and N. Ishii, The equations for modular function fields of principal congruence subgroups of prime level, Manuscripta Math. 90 (1996), no. 3, 271-285. https://doi.org/10.1007/BF02568306
- D. Kubert and S. Lang, Modular units, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 244, Springer-Verlag, New York-Berlin. 1981.
- Y. Lee and Y. K. Park, Modularity of a Ramanujan-Selberg continued fraction, J. Math. Anal. Appl. 438 (2016), no. 1, 373-394. https://doi.org/10.1016/j.jmaa.2016.01.065
- Y. Lee and Y. K. Park, A continued fraction of order twelve as a modular function, Math. Comp. 87 (2018), no. 312, 2011-2036. https://doi.org/10.1090/mcom/3259
- Y. Lee and Y. K. Park, Modular equations of a continued fraction of order six, Open Math. 17 (2019), no. 1, 202-219. https://doi.org/10.1515/math-2019-0003
- M. S. N. Mahadeva Naika, B. N. Dharmendra, and K. Shivashankara, A continued fraction of order twelve, Cent. Eur. J. Math. 6 (2008), no. 3, 393-404. https://doi.org/10.2478/s11533-008-0031-y
- S. Ramanujan, Notebooks, 2 volumes, Tata Institute of Fundamental Research, Bombay, 1957.
- M. S. Surekha, On the modular relations and dissections for a continued fraction of order sixteen, Palest. J. Math. 6 (2017), no. 1, 119-132.
- A. Vanitha, On the expansion of Ramanujan's continued fraction of order sixteen, Tamsui Oxf. J. Inf. Math. Sci. 31 (2016), no. 1, 81-99.
- K. R. Vasuki, N. Bhaskar, and G. Sharath, On a continued fraction of order six, Ann. Univ. Ferrara Sez. VII Sci. Mat. 56 (2010), no. 1, 77-89. https://doi.org/10.1007/s11565-010-0090-4