Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)

Liang-Cheng Zhang

Acta Arithmetica (1997)

  • Volume: 82, Issue: 4, page 379-392
  • ISSN: 0065-1036

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Liang-Cheng Zhang. "Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)." Acta Arithmetica 82.4 (1997): 379-392. <http://eudml.org/doc/207099>.

@article{Liang1997,
author = {Liang-Cheng Zhang},
journal = {Acta Arithmetica},
keywords = {Kronecker's limit formula; modular equations; Hilbert class field; Weber's invariant; Ramanujan's class invariants},
language = {eng},
number = {4},
pages = {379-392},
title = {Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)},
url = {http://eudml.org/doc/207099},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Liang-Cheng Zhang
TI - Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 4
SP - 379
EP - 392
LA - eng
KW - Kronecker's limit formula; modular equations; Hilbert class field; Weber's invariant; Ramanujan's class invariants
UR - http://eudml.org/doc/207099
ER -

References

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  1. [1] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991. Zbl0733.11001
  2. [2] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994. Zbl0785.11001
  3. [3] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997, to appear. Zbl0886.11001
  4. [4] 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
  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. J. Birch, Weber's class invariants, Mathematika 16 (1969), 283-294. Zbl0226.12005
  7. [7] D. A. Cox, Primes of the Form x² + ny², Wiley, New York, 1989. 
  8. [8] S. Lang, Elliptic Functions, 2nd ed., Springer, New York, 1987. 
  9. [9] K. Ramachandra, Some applications of Kronecker's limit formulas, Ann. of Math. 80 (1964), 104-148. Zbl0142.29804
  10. [10] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89. Zbl0682.12002
  11. [11] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957. 
  12. [12] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372. Zbl45.1249.01
  13. [13] C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980. Zbl0478.10001
  14. [14] G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98. Zbl0005.00902
  15. [15] H. Weber, Lehrbuch der Algebra, Vol. III, 2nd ed., Braunschweig, 1908 (reprinted by Chelsea, New York, 1961). 
  16. [16] L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula and modular equations (II), in: Analytic Number Theory, Proceedings of a Conference in Honor of H. Halberstam, Birkhäuser, 1996, 817-838. Zbl0877.11062

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