正規勞倫級數之度量非齊次丟番圖逼近

Abstract

在近期的一篇論文中，Kim和Nakada證明了一個在有限體之下，正規勞倫級數之非齊次丟番圖逼近的Kurzweil定理。在這個計畫中，我們打算歸納出他們的結論。此外，我們打算證明強大數法則，以及討論一些對於逼近函數的種種限制下類似的結果。

In a recent paper, Kim and Nakada proved an analogue of Kurzweil’s theorem for metric inhomogeneous Diophantine approximation of formal Laurent series over a finite field. In this project, we intend to generalize their result to simultaneous inhomogeneous Diophantine approximation. Moreover, we plan to prove strong law of large numbers with error terms for the number of solutions and discuss similar results for various restrictions on the approximation function.