On some properties of modular polynomials for the lambda function. (English. Russian original) Zbl 1176.30013
Math. Notes 86, No. 2, 216-233 (2009); translation from Mat. Zametki 86, No. 2, 237-255 (2009).
Summary: We prove the existence of modular polynomials for the lambda function and present an asymptotic formula for the maximum of the moduli of their coefficients.
MSC:
| 30C10 | Polynomials and rational functions of one complex variable |
Keywords:
lambda function; modular polynomial; theta constant; Galois group; Farey series; algebraic numberReferences:
| [1] | K. Mahler, ”On the coefficients of transformation polynomials for the modular function,” Bull. Austral. Math. Soc. 10, 197–218 (1974). · Zbl 0269.10013 · doi:10.1017/S0004972700040831 |
| [2] | P. Cohen, ”On the coefficients of the transformation polynomials for the ellipticmodular function,” Math. Proc. Cambridge Philos. Soc. 95(3), 389–402 (1984). · Zbl 0541.10026 · doi:10.1017/S0305004100061697 |
| [3] | P. Grinspan, ”A measure of simultaneous approximation for quasi-modular functions,” Ramanujan J. 5(1), 21–45 (2001). · Zbl 1002.11062 · doi:10.1023/A:1011484927500 |
| [4] | S. Lang, Elliptic Functions (Addison-Wesley, Reading, Mass., 1973; Nauka, Moscow, 1984). |
| [5] | N. I. Akhiezer, Elements of the Theory of Elliptic Functions (Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moscow-Leningrad, 1948) [in Russian]. |
| [6] | G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Oxford Univ. Press, Oxford, 1979). · Zbl 0423.10001 |
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