On the exact degree of multi-cyclic extension of ${\mathbb{F}}_q(t)$

Abstract

Let $q$ be a power of a prime number $p$, $k={\mathbb{F}}_q(t)$ be the rational function field over finite field ${\mathbb{F}}_q$ and $K/k$ be a multi-cyclic extension of prime degree. In this paper we will give an exact formula for the degree of $K$ over $k$ by considering both Kummer and Artin-Schreier cases.

arXiv commentNotice that this paper will not be published. We put it on the arXiv, since we hope that some character sums estimations over ${\mathbb{F}}_q[t]$ in Sections 2 and 3 of this paper may be useful for someone in the future