论文标题
关于广义拉瓜多项式的加洛瓦理论和修剪指数
On the Galois Theory of Generalized Laguerre Polynomials and Trimmed Exponential
论文作者
论文摘要
受Schur在泰勒（Taylor）系列的工作的启发，我们研究了修剪指数的Galois理论$ f_ {n，n，n+k} = \ sum_ {i = 0}^{i = 0}^{k}^{k} {k} {k} \ frac {x^^^^^i} {i}} {i}} {n+lag} = $ l^{（n）} _ k $ of度量$ k $。我们表明，如果$ n $是从$ \ {1，\ ldots，x \} $统一选择的，那么，几乎可以肯定的是，对于所有$ k \ leq x^{o（1）} $，$ f_ {n，n，n+k} $的$ f_ f _ {
Inspired by the work of Schur on the Taylor series of the exponential and Laguerre polynomials, we study the Galois theory of trimmed exponentials $f_{n,n+k}=\sum_{i=0}^{k} \frac{x^{i}}{(n+i)!}$ and of the generalized Laguerre polynomials $L^{(n)}_k$ of degree $k$. We show that if $n$ is chosen uniformly from $\{1,\ldots, x\}$, then, asymptotically almost surely, for all $k\leq x^{o(1)}$ the Galois groups of $f_{n,n+k}$ and of $L_{k}^{(n)}$ are the full symmetric group $S_k$.
