Zeros of Complete Symmetric Polynomials over Finite Fields

作     者：CAO Wei 

作者机构：School of Mathematics and StatisticsMinnan Normal UniversityZhangzhou 363000China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2024年第37卷第4期

页      面：1772-1788页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Natural Science Foundation of Fujian Province,China under Grant No.2022J02046 Fujian Key Laboratory of Granular Computing and Applications (Minnan Normal University) Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics 

主　　题：Complete symmetric polynomial finite field permutation polynomial value set 

摘      要：Wan and Zhang(2021) obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields,and proposed a problem whether their bound can be *** this paper,the author improves Wan-Zhang s bound from three *** proposed results are based on the estimates related to the number of certain permutations and the value sets of non-permutation polynomials associated to the complete symmetric *** the author believes that there are still possibilities to improve the bounds and hence Wan-Zhang s bound.