Radicals and units in Ramanujan's work

Bruce C. Berndt; Heng Huat Chan; Liang-Cheng Zhang

Acta Arithmetica (1998)

  • Volume: 87, Issue: 2, page 145-158
  • ISSN: 0065-1036

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Bruce C. Berndt, Heng Huat Chan, and Liang-Cheng Zhang. "Radicals and units in Ramanujan's work." Acta Arithmetica 87.2 (1998): 145-158. <http://eudml.org/doc/207210>.

@article{BruceC1998,
author = {Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang},
journal = {Acta Arithmetica},
keywords = {radicals; units; Chebyshev polynomial; Weber's class invariants; Ramanujan's singular moduli; hypergeometric function},
language = {eng},
number = {2},
pages = {145-158},
title = {Radicals and units in Ramanujan's work},
url = {http://eudml.org/doc/207210},
volume = {87},
year = {1998},
}

TY - JOUR
AU - Bruce C. Berndt
AU - Heng Huat Chan
AU - Liang-Cheng Zhang
TI - Radicals and units in Ramanujan's work
JO - Acta Arithmetica
PY - 1998
VL - 87
IS - 2
SP - 145
EP - 158
LA - eng
KW - radicals; units; Chebyshev polynomial; Weber's class invariants; Ramanujan's singular moduli; hypergeometric function
UR - http://eudml.org/doc/207210
ER -

References

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  1. [1] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994. Zbl0785.11001
  2. [2] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1998. Zbl0886.11001
  3. [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. Zbl0843.11007
  4. [4] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's singular moduli, Ramanujan J. 1 (1997), 53-74. Zbl0908.11024
  5. [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. Zbl0885.11058
  6. [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. Zbl0923.11159
  7. [7] B. C. Berndt and R. A. Rankin, Ramanujan: Letters and Commentary, Amer. Math. Soc., Providence, 1995; London Math. Soc., London, 1995. Zbl0842.01026
  8. [8] H. H. Chan and S.-S. Huang, On the Ramanujan-Gordon-Göllnitz continued fraction, Ramanujan J. 1 (1997), 75-90. Zbl0905.11008
  9. [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. [10] T. J. Osler, Cardan polynomials and the reduction of radicals, preprint. Zbl1002.12001
  11. [11] S. Ramanujan, Question 525, solution by N. S. Aiyar, J. Indian Math. Soc. 6 (1914), 191-192. 
  12. [12] S. Ramanujan, Question 682, solution by 'Zero', J. Indian Math. Soc. 7 (1915), 160. 
  13. [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. [14] S. Ramanujan, Question 1076, J. Indian Math. Soc. 11 (1919), 199. Zbl54.0105.05
  15. [15] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957. 
  16. [16] S. Ramanujan, Collected Papers, Chelsea, New York, 1962. 
  17. [17] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
  18. [18] G. N. Watson, Theorems stated by Ramanujan (XII): A singular modulus, J. London Math. Soc. 6 (1931), 65-70. Zbl0001.14601
  19. [19] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961. 
  20. [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. Zbl0877.11062

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