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DISTRIBUTION OF THE APPROXIMATION EXPONENTS OF A FAMILY OF POWER SERIES OVER A FINITE FIELD

  • Ayadi, Khalil (Universite de Sfax Faculte des Sciences Departement de Math ematiques) ;
  • Elouaer, Iheb (Universite de Sfax Faculte des Sciences Departement de Math ematiques)
  • Received : 2017.12.18
  • Accepted : 2018.07.05
  • Published : 2018.11.30

Abstract

In this paper, we exhibit the explicit forms of continued fraction expansions of a family of algebraic power series over a finite field and we study their asymptotic distribution of approximation exponents.

Keywords

References

  1. G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Co., Reading, MA, 1976.
  2. K. Ayadi, On the approximation exponent of some hyperquadratic power series, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 511-520.
  3. L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. (2) 103 (1976), no. 3, 593-610. https://doi.org/10.2307/1970953
  4. H.-J. Chen, Distribution of Diophantine approximation exponents for algebraic quantities in finite characteristic, J. Number Theory 133 (2013), no. 11, 3620-3644. https://doi.org/10.1016/j.jnt.2013.05.002
  5. A. Lasjaunias, Continued fractions for hyperquadratic power series over a finite field, Finite Fields Appl. 14 (2008), no. 2, 329-350. https://doi.org/10.1016/j.ffa.2007.01.001
  6. K. Mahler, On a theorem of Liouville in fields of positive characteristic, Canadian J. Math. 1 (1949), 397-400. https://doi.org/10.4153/CJM-1949-035-0
  7. B. de Mathan, Approximation exponents for algebraic functions in positive characteristic, Acta Arith. 60 (1992), no. 4, 359-370. https://doi.org/10.4064/aa-60-4-359-370
  8. W. M. Schmidt, On continued fractions and Diophantine approximation in power series fields, Acta Arith. 95 (2000), no. 2, 139-166. https://doi.org/10.4064/aa-95-2-139-166
  9. D. S. Thakur, Diophantine approximation exponents and continued fractions for algebraic power series, J. Number Theory 79 (1999), no. 2, 284-291. https://doi.org/10.1006/jnth.1999.2413
  10. D. S. Thakur, Function Field Arithmetic, World Scientific Publishing Co., Inc., River Edge, NJ, 2004.
  11. J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (1988), no. 3, 217-225. https://doi.org/10.1007/BF01850290