论文标题
优质学位的异常散射
Exceptional scatteredness in prime degree
论文作者
论文摘要
让$ q $是奇怪的素数，$ n $是一个正整数。令$ \ ell \ in \ mathbb f_ {q^n} [x] $为$ q $ linearized $ t $ scatter-scattered of Linearized $ r $。令$ d = \ max \ {t，r \} $为一个奇数的素数。在本文中，我们表明，在这些假设下，$ \ ell = x $。我们的技术涉及$ t $散布多项式的GALOIS理论表征，结合了有限字段$ \ mathbb f_q $的一般线性组的及传递子组的分类。
Let $q$ be an odd prime power and $n$ be a positive integer. Let $\ell\in \mathbb F_{q^n}[x]$ be a $q$-linearised $t$-scattered polynomial of linearized degree $r$. Let $d=\max\{t,r\}$ be an odd prime number. In this paper we show that under these assumptions it follows that $\ell=x$. Our technique involves a Galois theoretical characterization of $t$-scattered polynomials combined with the classification of transitive subgroups of the general linear group over the finite field $\mathbb F_q$.
