TY - JOUR

T1 - Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

AU - Berthé, V.

AU - Nakada, H.

AU - Natsui, R.

N1 - Funding Information:
✩ The authors are supported by the JSPS and CNRS 07 Sakura program. * Corresponding author. E-mail addresses: berthe@lirmm.fr (V. Berthé), nakada@math.keio.ac.jp (H. Nakada), natsui@fc.jwu.ac.jp (R. Natsui).

PY - 2008/11

Y1 - 2008/11

N2 - We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration.

AB - We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration.

KW - Laurent formal power series

KW - Metric Diophantine approximation

KW - Strong law of large numbers

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U2 - 10.1016/j.ffa.2008.03.001

DO - 10.1016/j.ffa.2008.03.001

M3 - Article

AN - SCOPUS:53649088486

VL - 14

SP - 849

EP - 866

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - 4

ER -