Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan

Acta Arithmetica (1992)

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

Abstract

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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 = ( A α q + B ) / ( C α q + D ) , where q is a power of p.

How to cite

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Bernard 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

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  1. [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
  2. [2] A. Blanchard et M. Mendès-France, Symétrie et transcendance, Bull. Sci. Math. 106 (3) (1982), 325-335. 
  3. [3] B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math. France. Mém. 21 (1970). Zbl0221.10037
  4. [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. [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. [6] Y. Taussat, Approximations diophantiennes dans un corps de séries formelles, Thèse de 3ème cycle, Bordeaux, 1986. 
  7. [7] S. Uchiyama, On the Thue-Siegel-Roth theorem III, Proc. Japan Acad. 36 (1960), 1-2. Zbl0098.03804
  8. [8] J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (3) (1988), 217-225. Zbl0661.10050

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