Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
Liang-Cheng Zhang
Acta Arithmetica, Tome 80 (1997), p. 379-392 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:207099 
@article{bwmeta1.element.bwnjournal-article-aav82i4p379bwm,
     author = {Liang-Cheng Zhang},
     title = {Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {379-392},
     zbl = {0890.11016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav82i4p379bwm}
}

Liang-Cheng Zhang. Ramanujan's class invariants, Kronecker's limit formula and modular equations (III). Acta Arithmetica, Tome 80 (1997) pp. 379-392. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav82i4p379bwm/

[000] [1] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991. | Zbl 0733.11001

[001] [2] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994. | Zbl 0785.11001

[002] [3] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997, to appear. | Zbl 0886.11001

[003] [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. | Zbl 0843.11007

[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. J. Birch, Weber's class invariants, Mathematika 16 (1969), 283-294. | Zbl 0226.12005

[006] [7] D. A. Cox, Primes of the Form x² + ny², Wiley, New York, 1989.

[007] [8] S. Lang, Elliptic Functions, 2nd ed., Springer, New York, 1987.

[008] [9] K. Ramachandra, Some applications of Kronecker's limit formulas, Ann. of Math. 80 (1964), 104-148. | Zbl 0142.29804

[009] [10] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89. | Zbl 0682.12002

[010] [11] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.

[011] [12] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372. | Zbl 45.1249.01

[012] [13] C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980. | Zbl 0478.10001

[013] [14] G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98. | Zbl 0005.00902

[014] [15] H. Weber, Lehrbuch der Algebra, Vol. III, 2nd ed., Braunschweig, 1908 (reprinted by Chelsea, New York, 1961).

[015] [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. | Zbl 0877.11062