Approximation exponents for algebraic functions in positive characteristic
Bernard de Mathan
Acta Arithmetica, Tome 62 (1992), p. 359-370 / Harvested from The Polish Digital Mathematics Library

In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type α=(Aαq+B)/(Cαq+D), where q is a power of p.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:206444
@article{bwmeta1.element.bwnjournal-article-aav60i4p359bwm,
     author = {Bernard de Mathan},
     title = {Approximation exponents for algebraic functions in positive characteristic},
     journal = {Acta Arithmetica},
     volume = {62},
     year = {1992},
     pages = {359-370},
     zbl = {0763.11048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav60i4p359bwm}
}
Bernard de Mathan. Approximation exponents for algebraic functions in positive characteristic. Acta Arithmetica, Tome 62 (1992) pp. 359-370. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav60i4p359bwm/

[000] [1] L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. 103 (1976), 593-610. | Zbl 0312.10024

[001] [2] A. Blanchard et M. Mendès-France, Symétrie et transcendance, Bull. Sci. Math. 106 (3) (1982), 325-335.

[002] [3] B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math. France. Mém. 21 (1970). | Zbl 0221.10037

[003] [4] W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), 388-404. | Zbl 0591.10021

[004] [5] C. F. Osgood, Effective bounds on the 'diophantine approximation' of algebraic functions over fields of arbitrary characteristic and applications to differential equations, Indag. Math. 37 (1975), 105-119. | Zbl 0302.10034

[005] [6] Y. Taussat, Approximations diophantiennes dans un corps de séries formelles, Thèse de 3ème cycle, Bordeaux, 1986.

[006] [7] S. Uchiyama, On the Thue-Siegel-Roth theorem III, Proc. Japan Acad. 36 (1960), 1-2. | Zbl 0098.03804

[007] [8] J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (3) (1988), 217-225. | Zbl 0661.10050