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

• Autorzy: Liang-Cheng Zhang
• Języki publikacji: EN

Kategorie tematyczne

• 11F32: Modular correspondences, etc.
• 11R39: Langlands-Weil conjectures, nonabelian class field theory
• 11F20: Dedekind eta function, Dedekind sums

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 4
• Strony: 379-392

Daty

wydano

1997

otrzymano

1997-02-21

poprawiono

1997-04-24

Twórcy

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 III, Springer, New York, 1991.
• [2] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
• [3] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997, to appear.
• [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.
• [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. J. Birch, Weber's class invariants, Mathematika 16 (1969), 283-294.
• [7] D. A. Cox, Primes of the Form x² + ny², Wiley, New York, 1989.
• [8] S. Lang, Elliptic Functions, 2nd ed., Springer, New York, 1987.
• [9] K. Ramachandra, Some applications of Kronecker's limit formulas, Ann. of Math. 80 (1964), 104-148.
• [10] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89.
• [11] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
• [12] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372.
• [13] C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980.
• [14] G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98.
• [15] H. Weber, Lehrbuch der Algebra, Vol. III, 2nd ed., Braunschweig, 1908 (reprinted by Chelsea, New York, 1961).
• [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.