有限域上完全对称多项式零点个数的一个注记  

A remark on the number of zeros of complete symmetric polynomials in nite elds

作　　者：张家瑜 谢炜涛 曹炜 ZHANG Jiayu;XIE Weitao;CAO Wei(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《纯粹数学与应用数学》2024年第4期571-580,共10页Pure and Applied Mathematics

基　　金：福建省自然科学基金(2022J02046).

摘　　要：设Fq为q元有限域,其中q=pr,p为素数.本文讨论了有限域Fq上完全对称多项式的零点个数问题.利用有限域上最小值集多项式的性质,给出了有限域上值集基数整除q的多项式形式,由此可改进已知关于有限域上完全对称多项式零点个数下界的估计.Let Fq be afinitefield with q elements,where q=pr,and p is a prime number.This paper discusses the problem about the number of zeros of complete symmetric polynomials in Fq.We utilize the properties of the minimum value set polynomials infinitefields tofind the forms of polynomials in Fq with the cardinality of the value sets dividing q,from which we can improve the known estimates on the lower bounds for the number of zeros of complete symmetric polynomials infinitefields.

关 键 词：有限域 完全对称多项式 零点个数 值集 

分 类 号：O156.1[理学—数学]