Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03548 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $f \in \mathbb{F}_{q}[x]$ be a polynomial of degree $d > 0$. Denote the image set of this polynomial as $V_{f}=\{f(α)\midα\in\mathbb{F}_{q}\}$ and denote the cardinality of this set as $N_{f}$. A much sharper bound for $N_{f}$ is established in this paper. In particular, for any $p\neq 2, 3$, and for nearly every generic quartic polynomial $f \in \mathbb{F}_{q}[x]$, we obtain $$\lvert N_f - \frac{5}{8} q \rvert \leq \frac{1}{2}\sqrt{q} + \frac{15}{4},$$ which holds as a simple corollary of the main result.