On enumeration of irreducible polynomials and related objects over a finite field with respect to their trace and norm

被引：0
作者：
Gao, Zhicheng [1 ]
Kuttner, Simon [1 ]
Wang, Qiang [1 ]
机构：
[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2021年 / 69卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Irreducible polynomials; Trace; Norm; Gauss sum; Mean; Variance; PRESCRIBED TRACE; ELLIPTIC-CURVES; ELEMENTS; NUMBER; GF(2); SUMS;
D O I：
10.1016/j.ffa.2020.101770
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we enumerate irreducible polynomials of degree m and related objects over a finite field F-q with respect to their trace and norm. Our approach makes use of both generating functions and exponential sums, and we improve all previously known results in the literature when m > root q. (c) 2020 Elsevier Inc. All rights reserved.
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页数：25
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