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Distribution of the approximation exponents of a family of power series over a finite field

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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.

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.

참고문헌 (11)

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  6. K. Mahler, "On a theorem of Liouville in fields of positive characteristic", Canadian J. Math, 1, pp.397~400 (1949)
  7. B. de Mathan, "Approximation exponents for algebraic functions in positive character-istic", Acta Arith, 60(4), pp.359~370 (1992)
  8. W. M. Schmidt, "On continued fractions and Diophantine approximation in power series elds", Acta Arith, 95(2), pp.139~166 (2000)
  9. D. S. Thakur, "Diophantine approximation exponents and continued fractions for alge-braic power series", J. Number Theory, 79(2), pp.284~291 (1999)
  10. D. S. Thakur, "Function Field Arithmetic" (2004), World Scientific Publishing Co., Inc.
  11. J. F. Voloch, "Diophantine approximation in positive characteristic", Period. Math. Hun-gar, 19(3), pp.217~225 (1988)

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