Abstract
Let $p$ be the characteristic of $\mathbb{F}_q$ and let $q$ be a primitive root modulo a prime $r = 2n + 1$. Let $\beta \in \mathbb{F}_{q^{2n}}$ be a primitive $r$th root of unity. We prove that the multiplicative order of the Gauss period $\beta + \beta^{-1}$ is at least $(\log p)^{c\log n}$ for some $c \gt 0$. This improves the bound obtained by Ahmadi, Shparlinski and Voloch when $p$ is very large compared with $n$. We also obtain bounds for "most" $p$.
Citation
Mei-Chu Chang. "ORDER OF GAUSS PERIODS IN LARGE CHARACTERISTIC." Taiwanese J. Math. 17 (2) 621 - 628, 2013. https://doi.org/10.11650/tjm.17.2013.2307
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