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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topBruce 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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- [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
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- [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. Zbl54.0105.05
- [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- [17] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
- [18] G. N. Watson, Theorems stated by Ramanujan (XII): A singular modulus, J. London Math. Soc. 6 (1931), 65-70. Zbl0001.14601
- [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. Zbl0877.11062
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