Radicals and units in Ramanujan's work
Bruce C. Berndt ; Heng Huat Chan ; Liang-Cheng Zhang
Acta Arithmetica, Tome 84 (1998), p. 145-158 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207210
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     author = {Bruce C. Berndt and Heng Huat Chan and Liang-Cheng Zhang},
     title = {Radicals and units in Ramanujan's work},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {145-158},
     zbl = {0919.11069},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav87i2p145bwm}
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Bruce C. Berndt; Heng Huat Chan; Liang-Cheng Zhang. Radicals and units in Ramanujan's work. Acta Arithmetica, Tome 84 (1998) pp. 145-158. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav87i2p145bwm/

[000] [1] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994. | Zbl 0785.11001

[001] [2] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1998. | Zbl 0886.11001

[002] [3] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants and cubic continued fraction, Acta Arith. 73 (1995), 67-85. | Zbl 0843.11007

[003] [4] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's singular moduli, Ramanujan J. 1 (1997), 53-74. | Zbl 0908.11024

[004] [5] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula, and modular equations, Trans. Amer. Math. Soc. 349 (1997), 2125-2173. | Zbl 0885.11058

[005] [6] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's association with radicals in India, Amer. Math. Monthly 104 (1997), 913-919. | Zbl 0923.11159

[006] [7] B. C. Berndt and R. A. Rankin, Ramanujan: Letters and Commentary, Amer. Math. Soc., Providence, 1995; London Math. Soc., London, 1995. | Zbl 0842.01026

[007] [8] H. H. Chan and S.-S. Huang, On the Ramanujan-Gordon-Göllnitz continued fraction, Ramanujan J. 1 (1997), 75-90. | Zbl 0905.11008

[008] [9] S.-Y. Kang, Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions, Acta Arith., to appear.

[009] [10] T. J. Osler, Cardan polynomials and the reduction of radicals, preprint. | Zbl 1002.12001

[010] [11] S. Ramanujan, Question 525, solution by N. S. Aiyar, J. Indian Math. Soc. 6 (1914), 191-192.

[011] [12] S. Ramanujan, Question 682, solution by 'Zero', J. Indian Math. Soc. 7 (1915), 160.

[012] [13] S. Ramanujan, Question 1070, solutions by S. D. Chowla, N. B. Mitra, and S. V. Venkataraya Sastri, J. Indian Math. Soc. 11 (1919), 160.

[013] [14] S. Ramanujan, Question 1076, J. Indian Math. Soc. 11 (1919), 199. | Zbl 54.0105.05

[014] [15] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.

[015] [16] S. Ramanujan, Collected Papers, Chelsea, New York, 1962.

[016] [17] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. | Zbl 0639.01023

[017] [18] G. N. Watson, Theorems stated by Ramanujan (XII): A singular modulus, J. London Math. Soc. 6 (1931), 65-70. | Zbl 0001.14601

[018] [19] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.

[019] [20] L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula and modular equations (II), in: Analytic Number Theory, Proc. Conf. in Honor of Heini Halberstam, Vol. 2, B. C. Berndt, H. G. Diamond, and A. J. Hildebrand (eds.), Birkhäuser, Boston, 1996, 817-838. | Zbl 0877.11062