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
UR - http://www.scopus.com/inward/record.url?scp=53649088486&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=53649088486&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2008.03.001
DO - 10.1016/j.ffa.2008.03.001
M3 - Article
AN - SCOPUS:53649088486
SN - 1071-5797
VL - 14
SP - 849
EP - 866
JO - Finite Fields and their Applications
JF - Finite Fields and their Applications
IS - 4
ER -