Radicals and units in Ramanujan's work

• Autorzy: Bruce C. Berndt , Heng Huat Chan , Liang-Cheng Zhang
• Języki publikacji: EN

Kategorie tematyczne

• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 2
• Strony: 145-158

Daty

wydano

1998

otrzymano

1998-01-27

poprawiono

1998-06-15

Twórcy

autor

Bruce C. Berndt

• Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.

autor

Heng Huat Chan

• Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore

autor

Liang-Cheng Zhang

• Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804, U.S.A.

Bibliografia

• [1] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
• [2] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1998.
• [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.
• [4] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's singular moduli, Ramanujan J. 1 (1997), 53-74.
• [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.
• [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.
• [7] B. C. Berndt and R. A. Rankin, Ramanujan: Letters and Commentary, Amer. Math. Soc., Providence, 1995; London Math. Soc., London, 1995.
• [8] H. H. Chan and S.-S. Huang, On the Ramanujan-Gordon-Göllnitz continued fraction, Ramanujan J. 1 (1997), 75-90.
• [9] S.-Y. Kang, Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions, Acta Arith., to appear.
• [10] T. J. Osler, Cardan polynomials and the reduction of radicals, preprint.
• [11] S. Ramanujan, Question 525, solution by N. S. Aiyar, J. Indian Math. Soc. 6 (1914), 191-192.
• [12] S. Ramanujan, Question 682, solution by 'Zero', J. Indian Math. Soc. 7 (1915), 160.
• [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.
• [14] S. Ramanujan, Question 1076, J. Indian Math. Soc. 11 (1919), 199.
• [15] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
• [16] S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
• [17] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
• [18] G. N. Watson, Theorems stated by Ramanujan (XII): A singular modulus, J. London Math. Soc. 6 (1931), 65-70.
• [19] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.
• [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.