A generalization of the sizes of differential equations and its applications to G -function theory

Makoto Nagata

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)

  • Volume: 30, Issue: 2, page 465-497
  • ISSN: 0391-173X

How to cite

top

Nagata, Makoto. "A generalization of the sizes of differential equations and its applications to $G$-function theory." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 30.2 (2001): 465-497. <http://eudml.org/doc/84449>.

@article{Nagata2001,
author = {Nagata, Makoto},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {size of a matrix; size of a solution; -function; height},
language = {eng},
number = {2},
pages = {465-497},
publisher = {Scuola normale superiore},
title = {A generalization of the sizes of differential equations and its applications to $G$-function theory},
url = {http://eudml.org/doc/84449},
volume = {30},
year = {2001},
}

TY - JOUR
AU - Nagata, Makoto
TI - A generalization of the sizes of differential equations and its applications to $G$-function theory
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2001
PB - Scuola normale superiore
VL - 30
IS - 2
SP - 465
EP - 497
LA - eng
KW - size of a matrix; size of a solution; -function; height
UR - http://eudml.org/doc/84449
ER -

References

top
  1. [1] Y. André, "G-functions and Geometry", Max-Planck-Institut, Bonn, 1989. Zbl0688.10032MR990016
  2. [2] A. Baker, "Transcendental Number Theory", Cambridge University Press, Cambridge, 1975. Zbl0297.10013MR422171
  3. [3] E. Bombieri, On G-functions, Recent progress in analytic number theory 2Academic Press, New York (1981), 1-67. Zbl0461.10031MR637359
  4. [4] G. Christol - B. Dwork, Differential modules of bounded spectral norms, Contemp. Math.133 (1992), 39-58. Zbl0765.12003MR1183969
  5. [5] G. Christol - B. Dwork, Effective p-adic bounds at regular singular points, Duke Math. J.62 (1991), 689-720. Zbl0762.12004MR1104814
  6. [6] D.V. Chudnovsky - G.V. Chudnovsky, Applications of Padé approximations to diophantine inequalities in values of G-functions, Lect. Notes in Math. 1135, Springer-Verlag, Berlin, Heidelberg, New York, (1985), 9-51. Zbl0561.10016MR803349
  7. [7] G.V. Chudnovsky, On applications of diophantine approximations, Proc. Nat. Acad. Sci. U.S.A.81 (1984), 1926-1930. Zbl0544.10034MR768160
  8. [8] B. Dwork - G. Gerotto - F.J. Sullivan, "An Introduction to G-functions", Annals of Math. Studies133 (1994), Princeton University Press, Princeton, New Jersey. Zbl0830.12004MR1274045
  9. [9] A.I. Galo, "Estimates from below of polynomials in the values of analytic functions of a certain class", Math. USSR Sbornik24 (1974), 385-407, Original article in Math. Sbornik95 (137) (1974), 396-417. Zbl0318.10023
  10. [10] X. Guangshan, On the arithmetic properties of G-functions, International symposium in memory of Hua Loo Keng (Number theory)1 (1991), Springer-Verlag, Berlin, Heidelberg, New York, 331-346. Zbl0831.11035MR1135820
  11. [11] K. Mahler, "Lectures on Transcendental Numbers", Lect. Notes in Math.546 (1976), Springer-Verlag, Berlin, Heidelberg, New York. Zbl0332.10019MR491533
  12. [12] K. Mahler, Perfect systems, Compositio Math.19 (1968), 95-166. Zbl0168.31303MR239099
  13. [13] M. Nagata, Sequences of differential systems, Proc. Amer. Math. Soc.124 (1996), 21-25. Zbl0858.12005MR1286002
  14. [14] A.B. Shidlovskii, "Transcendental Numbers", Walter de Gruyter, Berlin, New York, 1989. Zbl0689.10043MR1033015
  15. [15] K. Väänänen, On linear forms of a certain class of G-functions and p-adic G-functions, Acta Arith.36 (1980), 273-295. Zbl0369.10021MR581376
  16. [16] C.L. Siegel, "Über einige Anwendungen diophantischer Approximationen ", Abh. Preuss. Akad. Wiss., Phys. Math. Kl. nr.1 (1929). Zbl56.0180.05JFM56.0180.05

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.