# Approximation exponents for algebraic functions in positive characteristic

Acta Arithmetica (1992)

- Volume: 60, Issue: 4, page 359-370
- ISSN: 0065-1036

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topBernard de Mathan. "Approximation exponents for algebraic functions in positive characteristic." Acta Arithmetica 60.4 (1992): 359-370. <http://eudml.org/doc/206444>.

@article{BernarddeMathan1992,

abstract = {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 $α = (Aα^q+B)/(Cα^q+D)$, where q is a power of p.},

author = {Bernard de Mathan},

journal = {Acta Arithmetica},

keywords = {algebraic numbers; positive characteristic; rational approximations; algebraic functions; field of formal Laurent series; approximation exponent},

language = {eng},

number = {4},

pages = {359-370},

title = {Approximation exponents for algebraic functions in positive characteristic},

url = {http://eudml.org/doc/206444},

volume = {60},

year = {1992},

}

TY - JOUR

AU - Bernard de Mathan

TI - Approximation exponents for algebraic functions in positive characteristic

JO - Acta Arithmetica

PY - 1992

VL - 60

IS - 4

SP - 359

EP - 370

AB - 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 $α = (Aα^q+B)/(Cα^q+D)$, where q is a power of p.

LA - eng

KW - algebraic numbers; positive characteristic; rational approximations; algebraic functions; field of formal Laurent series; approximation exponent

UR - http://eudml.org/doc/206444

ER -

## References

top- [1] L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. 103 (1976), 593-610. Zbl0312.10024
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- [3] B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math. France. Mém. 21 (1970). Zbl0221.10037
- [4] W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), 388-404. Zbl0591.10021
- [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. Zbl0302.10034
- [6] Y. Taussat, Approximations diophantiennes dans un corps de séries formelles, Thèse de 3ème cycle, Bordeaux, 1986.
- [7] S. Uchiyama, On the Thue-Siegel-Roth theorem III, Proc. Japan Acad. 36 (1960), 1-2. Zbl0098.03804
- [8] J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (3) (1988), 217-225. Zbl0661.10050

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