논문KCI 등재
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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- H. -J. Chen, "Distribution of Diophantine approximation exponents for algebraic quanti-ties in finite characteristic", J. Number Theory, 133(11), pp.3620~3644 (2013)
- A. Lasjaunias, "Continued fractions for hyperquadratic power series over a finite field", Finite Fields Appl, 14(2), pp.329~350 (2008)
- K. Mahler, "On a theorem of Liouville in fields of positive characteristic", Canadian J. Math, 1, pp.397~400 (1949)
- B. de Mathan, "Approximation exponents for algebraic functions in positive character-istic", Acta Arith, 60(4), pp.359~370 (1992)
- W. M. Schmidt, "On continued fractions and Diophantine approximation in power series elds", Acta Arith, 95(2), pp.139~166 (2000)
- D. S. Thakur, "Diophantine approximation exponents and continued fractions for alge-braic power series", J. Number Theory, 79(2), pp.284~291 (1999)
- D. S. Thakur, "Function Field Arithmetic" (2004), World Scientific Publishing Co., Inc.
- J. F. Voloch, "Diophantine approximation in positive characteristic", Period. Math. Hun-gar, 19(3), pp.217~225 (1988)
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