ArticleOriginal scientific text
Title
Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
Authors 1
Affiliations
- Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804, U.S.A.
Bibliography
- B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991.
- B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
- B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997, to appear.
- B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants and cubic continued fraction, Acta Arith. 73 (1995), 67-85.
- 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.
- B. J. Birch, Weber's class invariants, Mathematika 16 (1969), 283-294.
- D. A. Cox, Primes of the Form x² + ny², Wiley, New York, 1989.
- S. Lang, Elliptic Functions, 2nd ed., Springer, New York, 1987.
- K. Ramachandra, Some applications of Kronecker's limit formulas, Ann. of Math. 80 (1964), 104-148.
- K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89.
- S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
- S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372.
- C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980.
- G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98.
- H. Weber, Lehrbuch der Algebra, Vol. III, 2nd ed., Braunschweig, 1908 (reprinted by Chelsea, New York, 1961).
- 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.
Pages:
379-392
Main language of publication
English
Received
1997-02-21
Accepted
1997-04-24
Published
1997
Exact and natural sciences