论文标题
同时合理近似与$ p $ adig数字及其整体功能，ii
On simultaneous rational approximation to a $p$-adic number and its integral powers, II
论文作者
论文摘要
令$ p $为主要数字。对于一个正整数$ n $和一个实数$ξ$，令$λ_n（ξ）$表示实际数字$λ$的至上x_0ξ-x_1 | _p，\ ldots，| x_0ξ^n-x_n | _p $都小于$ x^{--λ-1} $，其中$ x $是$ | x_0 |，| x_1 |，\ ldots，| x_n | $的最大值。我们在$λ_n（ξ）$等于（或大于或等于）给定值的$λ_n（ξ）$的hausdorff尺寸上建立了新的结果。
Let $p$ be a prime number. For a positive integer $n$ and a real number $ξ$, let $λ_n (ξ)$ denote the supremum of the real numbers $λ$ for which there are infinitely many integer tuples $(x_0, x_1, \ldots , x_n)$ such that $| x_0 ξ- x_1|_p, \ldots , | x_0 ξ^n - x_n|_p$ are all less than $X^{-λ- 1}$, where $X$ is the maximum of $|x_0|, |x_1|, \ldots , |x_n|$. We establish new results on the Hausdorff dimension of the set of real numbers $ξ$ for which $λ_n (ξ)$ is equal to (or greater than or equal to) a given value.
