正特徵域上丟番圖逼近的賦距結果

Abstract

摘要：近來的研究文獻，H. Nakada and R. Natsui 在正規Laurent 級數域上考慮─ 沒有互質條件下的丟番圖逼近(Diophantine approximation)，得到其解的個數滿足 強大數法則。利用早先W. M. Schmidt 所提出的方法，他們的結果是非常可能有 相當程度地增進。在這個計畫中，我們將在非齊次丟番圖逼近、有限丟番圖逼近 及同時丟番圖逼近，研究類似的問題，並發展出較增進的結果。

Abstract. In a recent paper, H. Nakada and R. Natsui considered the Diophantine approximation problem in the field of formal Laurent series without the coprimeness condition and obtained a strong law of large numbers for the number of solutions. By using an old method due to W. M. Schmidt, it is very likely that their result can be considerable improved. In this project, we intend to work out such an improvement as well as investigate similar questions for inhomogeneous Diophantine approximation, restricted Diophantine approximation, and simultaneous Diophantine approximation.