TY - JOUR

T1 - A refined Kurzweil type theorem in positive characteristic

AU - Kim, Dong Han

AU - Nakada, Hitoshi

AU - Natsui, Rie

N1 - Funding Information:
E-mail addresses: kim2010@dongguk.edu (D.H. Kim), nakada@math.keio.ac.jp (H. Nakada), natsui@fc.jwu.ac.jp (R. Natsui). 1 Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A2004473). 2 Hitoshi Nakada was partially supported by Grant-in Aid for Scientific research (No. 21340027) by Japan Society for the Promotion of Science. 3 Rie Natsui was partially supported by Grant-in Aid for Scientific research (No. 23740088) by Japan Society for the Promotion of Science.

PY - 2013/3

Y1 - 2013/3

N2 - We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (ℓn) that there are infinitely many polynomials P and Q such that |Qf-P-g|n-ℓn, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (ℓn) with Σq- ℓn=∞ there are infinitely many solutions for almost every g.

AB - We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (ℓn) that there are infinitely many polynomials P and Q such that |Qf-P-g|n-ℓn, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (ℓn) with Σq- ℓn=∞ there are infinitely many solutions for almost every g.

KW - Formal Laurent series

KW - Inhomogeneous Diophantine approximation

KW - Kurzweil type theorem

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U2 - 10.1016/j.ffa.2012.12.002

DO - 10.1016/j.ffa.2012.12.002

M3 - Article

AN - SCOPUS:84873151037

SN - 1071-5797

VL - 20

SP - 64

EP - 75

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

IS - 1

ER -