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On the arithmetic properties of the values of G-functions

Published online by Cambridge University Press:  09 April 2009

K. Väänänen  and
Xu Guangshan
K. Väänänen
Affiliation:
Department of Mathematics, University of Oulu, Oulu, Finland
Xu Guangshan
Affiliation:
Institute of Mathematics, Academia Sinica Beijing, China
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Abstract

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In a recent paper Chudnovsky considered the arithmetic properties of certain values of classical Siegel G-function solutions of a system of linear homogeneous differential equations without any restrictive conditions. The present paper generalizes some results of Chudnovsky in both the archimedian and the p-adic case.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 1 , August 1989 , pp. 71 - 82
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bertrand, D. and Beukers, F., ‘Équations différentielles linéaires et majorations de multiplicités’, Ann. Sci. École Norm. Sup. 18 (1985), 181–192.Google Scholar
[2]Bombieri, E., ‘On G-functions’, Recent progress in analytic number theory, Vol. II, edited by Halberstam, H. and Hooley, C. (Academic Press, 1981).Google Scholar
[3]Chudnovsky, G. V., ‘On applications of diophantine approximations’, Proc. Nat. Acad. Sci. U.S.A. 8 (1984), 7261–7265.Google Scholar
[4]Flicker, Y., ‘On p-adic G-functions’, J. London Math. Soc. 15 (1977), 395–402.CrossRefGoogle Scholar
[5]Galochkin, A. I., ‘Lower bounds for polynomials of the values of the class of analytic functions’, Mat. Sb. 95 (137) (3) (1974), 396–417.Google Scholar
[6]Matveev, E. M., ‘Linear forms in the values of G-functions, and diophantine equations’, Mat. Sb. 117 (159) (3) (1982), 379–396.Google Scholar
[7]Nesterenko, Yu. V., ‘Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers’, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 239–270.Google Scholar
[8]Nurmagomedov, M. S., ‘The arithmetic properties of the values of G-functions’, Vestnik Moskov. Univ. Ser. I, Mat. Meh. 26 (6) (1971), 79–86.Google Scholar
[9]Siegel, C. L., ‘Uber einige Anwendungen diophantischer Approximationen’, Abh. Preuss. Akad. Wiss., Phys.-Mat. Kl. No.1 (1929).Google Scholar
[10]Väänänen, K., ‘On linear forms of a certain class of G-functions and p-adic G-functions’, Acta Arith. 36 (1980), 273–295.Google Scholar
[11]Väänänen, K., ‘On the arithmetic properties of p-adic G-functions’, Arch. Math. 35 (1980), 364–373.Google Scholar
[12]Väänänen, K., ‘On a class of G-functions’, Mathematics, University of Oulu 1/81, 1981.Google Scholar
[13]Väänänen, K., ‘On a class of G-functions’, Progress in mathematics, 38, edited by Coates, J. and Helgason, S. (Birkhäuser, 1983).Google Scholar
[14]Väänänen, K. and Guangshan, Xu, ‘On linear forms of G-functions’, Acta Arith. 50 (1988), 251–263.Google Scholar
[15]Guangshan, Xu, ‘On lower estimate of linear forms involving a class of G-functions’, Acta Math. Sinica 24 (1981), 578–586.Google Scholar
[16]Guangshan, Xu., ‘A note on linear forms in a class of E-functions and G-functions’, J. Austral. Math. Soc. Ser. A 35 (1983), 338–348.Google Scholar