Zeros of Complete Symmetric Polynomials over Finite Fields  

作　　者：CAO Wei 

机构地区：[1]School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China

出　　处：《Journal of Systems Science & Complexity》2024年第4期1772-1788,共17页系统科学与复杂性学报（英文版）

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。

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 improved.In this paper,the author improves Wan-Zhang's bound from three aspects.The 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 polynomial.And the author believes that there are still possibilities to improve the bounds and hence Wan-Zhang's bound.

关 键 词：Complete symmetric polynomial finite field permutation polynomial value set 

分 类 号：O174.14[理学—数学]