A refined Kurzweil type theorem in positive characteristic
A refined Kurzweil type theorem in positive characteristic
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DOI：
10.1016/j.ffa.2012.12.002
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
Dong Han Kim;H. Nakada;Rie Natsui
中科院分区：
文献类型：
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作者：
Dong Han Kim;H. Nakada;Rie Natsui
考虑了一类单调逼近序列在形式Laurent级数域中的库兹韦尔型非齐次丢芬图近似定理。我们找到了无理数f和单调递增（r n）的一个充分必要条件，即对于几乎每一个g都有无穷多个多项式P和Q，使得[公式：见文]n=deg(Q)。我们还研究了无理数f的一些条件，使得对于所有单调递增（r n）有[公式：见文]，几乎每一个g都有无穷多个解。
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 [Formula: see text] , n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (ℓn) with [Formula: see text] there are infinitely many solutions for almost every g.