四川大学学报（自然科学版）2023，Vol.60Issue(3)：21-25,5.DOI:10.19907/j.0490-6756.2023.031004
一类广义Schur型多项式的不可约性
On the irreducibility of a class of generalized Schur-type polynomials
摘要
Abstract
Let n be a positive integer and a1,…,an ∈Z.Schur proved that the polynomial 1+a1x+a2x2/2!+…+an-1xn-1/(n-1)!+anxa/n!is irreducible over Q by using the factorization of prime ideal,where paper,we study the irreducibility of the generalized Schur-type polynomial 1+x+++…+paper,we study the irreducibility of the generalized Schur-type polynomial 1+x+x2/2+x3/6+…+xpa/pa(pa-1).By using the tool of p-adic Newton polygon and applying the local-global principle,we prove the irreducibility of this polynomial,where p is a prime number and a is a positive integer.关键词
不可约/p-adic牛顿多边形/局部整体原则Key words
Irreducibility/p-adic Newton polygon/Local-global principle分类
数理科学引用本文复制引用
尹轩睿,吴荣军,朱光艳..一类广义Schur型多项式的不可约性[J].四川大学学报（自然科学版）,2023,60(3):21-25,5.基金项目
西南民族大学科研启动金资助项目(RQD2021100) （RQD2021100）
四川省自然科学基金(2022NSFSC1830) （2022NSFSC1830）
