Year: 2022
Author: Xiwang Cao, Liqin Qian
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 184–205
Abstract
Let $\mathbb{F}_q$ be a finite field and $\mathbb{F}_{q^s}$ be an extension of $\mathbb{F}_q$. Let $f(x)\in \mathbb{F}_q[x]$ be a polynomial of degree $n$ with ${\rm gcd}(n,q) = 1$. We present a recursive formula for evaluating the exponential sum $\sum_{c\in \mathbb{F}_{q^s}} \chi^{(s)}(f(x))$. Let $a$ and $b$ be two elements in $\mathbb{F}_q$ with a $a≠0$, $u$ be a positive integer. We obtain an estimate for the exponential sum $\sum_{c\in \mathbb{F}^∗_{q^s}}\chi^{(s)} (ac^u+bc^{−1})$, where $\chi^{(s)}$ is the lifting of an additive character $\chi$ of $\mathbb{F}_q$. Some properties of the sequences constructed from these exponential sums are provided too.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0030
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 184–205
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Exponential sums finite fields Dickson polynomials sequences.