Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sequences of differential systems


Author: Makoto Nagata
Journal: Proc. Amer. Math. Soc. 124 (1996), 21-25
MSC (1991): Primary 12H25; Secondary 11S99
MathSciNet review: 1286002
Full-text PDF Free Access

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).


References [Enhancements On Off] (What's this?)

  • 1. Yves André, 𝐺-functions and geometry, Aspects of Mathematics, E13, Friedr. Vieweg & Sohn, Braunschweig, 1989. MR 990016 (90k:11087)
  • 2. E. Bombieri, On 𝐺-functions, Recent progress in analytic number theory, Vol. 2 (Durham, 1979) Academic Press, London-New York, 1981, pp. 1–67. MR 637359 (83c:10050)
  • 3. D. V. Chudnovsky and G. V. Chudnovsky, Applications of Padé approximations to Diophantine inequalities in values of 𝐺-functions, Number theory (New York, 1983–84) Lecture Notes in Math., vol. 1135, Springer, Berlin, 1985, pp. 9–51. MR 803349 (87a:11062), http://dx.doi.org/10.1007/BFb0074600
  • 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 (1968). MR 0239099 (39 #458)
  • 7. Andrei Borisovich Shidlovskii, Transcendental numbers, de Gruyter Studies in Mathematics, vol. 12, Walter de Gruyter & Co., Berlin, 1989. Translated from the Russian by Neal Koblitz; With a foreword by W. Dale Brownawell. MR 1033015 (90j:11066)
  • 8. Keijo Väänänen, On linear forms of a certain class of 𝐺-functions and 𝑝-adic 𝐺-functions, Acta Arith. 36 (1980), no. 3, 273–295. MR 581376 (82b:10045)

Similar Articles

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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society