@article {
author = {Sharma, Rajendra Kumar and Takshak, Soniya and Awasthi, Ambrish and Sharma, Hariom},
title = {Existence of rational primitive normal pairs over finite fields},
journal = {International Journal of Group Theory},
volume = {13},
number = {1},
pages = {17-30},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2022.133016.1784},
abstract = {For a finite field $𝔽_{q^n}$ and a rational function $f=\frac{f_1}{f_2} \in 𝔽_{q^n}(x)$, we present a sufficient condition for the existence of a primitive normal element $\alpha \in 𝔽_{q^n}$ in such a way $f(\alpha)$ is also primitive in $𝔽_{q^n}$, where $f(x)$ is a rational function in $𝔽_{q^n}(x)$ of degree sum $m$ (degree sum of $f(x)=\frac{f_1(x)}{f_2(x)}$ is defined to be the sum of the degrees of $f_1(x)$ and $f_2(x)$). Additionally, for rational functions of degree sum 4, we proved that there are only $37$ and $16$ exceptional values of $(q,n)$ when $q=2^k$ and $q=3^k$ respectively.},
keywords = {finite field,Primitive Element,Normal Element,character},
url = {https://ijgt.ui.ac.ir/article_26751.html},
eprint = {https://ijgt.ui.ac.ir/article_26751_6cae12cb2576f93d62038c4373869632.pdf}
}