Sequences of differential systems

Author:
Makoto Nagata

Journal:
Proc. Amer. Math. Soc. **124** (1996), 21-25

MSC (1991):
Primary 12H25; Secondary 11S99

DOI:
https://doi.org/10.1090/S0002-9939-96-03013-4

MathSciNet review:
1286002

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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).

**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
12H25,
11S99

Retrieve articles in all journals with MSC (1991): 12H25, 11S99

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:
https://doi.org/10.1090/S0002-9939-96-03013-4

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

Article copyright:
© Copyright 1996
American Mathematical Society