@Article{CMR-38-184,
author = {Cao , Xiwang and Qian , Liqin},
title = {A Recursive Formula and an Estimation for a Specific Exponential Sum},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {38},
number = {2},
pages = {184--205},
abstract = {<p style="text-align: justify;">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 <span style="text-align: justify;">$\mathbb{F}_q$</span>. Some properties of the sequences constructed from
these exponential sums are provided too.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2021-0030},
url = {http://global-sci.org/intro/article_detail/cmr/20270.html}
}