Abstract
In this paper, we give the p–adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.
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Barré, K., Diaz, G., Gramain, F., Philibert, G.: Une preuve de la conjecture de Mahler–Manin. Invent. Math., 124, 1–9 (1996)
Barré, K.: Measure d’approximation simultanée de q et J(q). J. Number Theory, 66, 102–128 (1997)
Nesterenko, Yu. V.: Modular functions and transcendence problems. Mat. Sb., 187(9), 65–96 (1996)
Nesterenko, Yu. V.: on the measure of algebraic independence of the values of Ramanujan functions. Proceedings of the Steklov Institute of Math., 218, 294–331 (1997)
Nesterenko, Yu. V.: Algebraic independence for values of Ramanujan functions, Introduction to algebraic independence theory, Edited by Nesterenko Yu. V. and Philippon P., Lecture Notes in Math. 1752, 27–46, Springer, Berlin, Heidelberg, New York, 2001
Adams, W. W.: Transcendental numbers in the p–adic domain. Amer. J. Math., 88, 279–308 (1966)
Wang, T. Q.: p–adic transcendence and p–adic transcendence measures for the values of Mahler type functions. Acta Math. Sinica, English Series, 22(1), 187–194 (2006)
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Supported by the NSFC (No. 10171097; 10571180)
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Wang, T.Q., Xu, G.S. p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions. Acta Math Sinica 23, 83–88 (2007). https://doi.org/10.1007/s10114-005-0708-0
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DOI: https://doi.org/10.1007/s10114-005-0708-0