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Sequences of differential systems
Author(s):
Makoto
Nagata
Journal:
Proc. Amer. Math. Soc.
124
(1996),
21-25.
MSC (1991):
Primary 12H25;
Secondary 11S99
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Abstract:
Our main result deals with certain properties of the sizes of a differential system and its dual system. It represents an improvement of part of the results in André's G-function theory (Max-Planck-Institut, Bonn, 1989).
References:
- 1.
- Y. André, G-functions and Geometry, Max-Planck-Institut, Bonn, 1989. MR 90k:11087
- 2.
- E. Bombieri, On G-functions, Recent Progress in Analytic Number Theory, Vol. 2, Academic Press, New York, 1981, pp. 1--67. MR 83c:10050
- 3.
- D.V. Chudnovsky and G.V. Chudnovsky, Applications of Padé approximations to diophantine inequalities in values of G-functions, Lecture Notes in Math., vol. 1135, Springer-Verlag, Berlin, Heidelberg, and New York, 1985, pp. 9--51. MR 87a:11062
- 4.
- A.I. Galochkin, Estimates from below of polynomials in the values of analytic functions of a certain class, Math. USSR-Sb. 24 (1974), 385--407; Original article in Mat. Sb., 95 (137) (1974), 396--417.
- 5.
- X. Guangshan, On the arithmetic properties of G-functions, International Symposium in Memory of Hua Loo Keng (Number Theory), Springer-Verlag, Berlin, Heidelberg, and New York, 1991, pp. 331--346.
- 6.
- K. Mahler, Perfect systems, Compositio Math. 19 (1968), 95--166. MR 39:458
- 7.
- A.B. Shidlovskii, Transcendental numbers, Walter de Gruyter, Berlin and New York, 1989. MR 90j:11066
- 8.
- K. Väänänen, On linear forms of a certain class of G-functions and p-adic G-functions, Acta Arith. 36 (1980), 273--295. MR 82b:10045
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Additional Information:
Makoto
Nagata
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo, 152, Japan
Email:
nagata@math.titech.ac.jp
DOI:
10.1090/S0002-9939-96-03013-4
PII:
S 0002-9939(96)03013-4
Keywords:
G-functions
Received by editor(s):
October 25, 1993
Received by editor(s) in revised form:
July 15, 1994
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
1996,
American Mathematical Society
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