论文标题
约束的双苯胺近似
Diophantine approximation with constraints
论文作者
论文摘要
在Schmidt，Thurnheer和Bugeaud-Kristensen之后，我们研究Dirichlet的线性形式定理是如何需要修改的。假设我们正在近似$ \ mathbb {r}^n $的点具有线性独立的坐标，超过$ \ mathbb {q} $，我们获得了近似值的最佳可能指数，这仅取决于$ v $的尺寸。我们的估计值是通过减少到Thurnheer的结果来得出的，而它们的最优性来自于涉及角约束的数字的参数几何形状的新一般结构。
Following Schmidt, Thurnheer and Bugeaud-Kristensen, we study how Dirichlet's theorem on linear forms needs to be modified when one requires that the vectors of coefficients of the linear forms make a bounded acute angle with respect to a fixed proper non-zero subspace $V$ of $\mathbb{R}^n$. Assuming that the point of $\mathbb{R}^n$ that we are approximating has linearly independent coordinates over $\mathbb{Q}$, we obtain best possible exponents of approximation which surprisingly depend only on the dimension of $V$. Our estimates are derived by reduction to a result of Thurnheer, while their optimality follows from a new general construction in parametric geometry of numbers involving angular constraints.
