Value Sets of Sparse Polynomials

We obtain a new lower bound on the size of the value set $\mathscr{V}(f)=f(\mathbb{F}_{p})$ of a sparse polynomial $f\in \mathbb{F}_{p}[X]$ over a finite field of $p$ elements when $p$ is prime. This bound is uniform with respect to the degree and depends on some natural arithmetic properties of the...

Full description

Saved in:
Bibliographic Details
Published in:Canadian mathematical bulletin 2020-03, Vol.63 (1), p.187-196
Main Authors: Shparlinski, Igor E., Voloch, José Felipe
Format: Article
Language:English
Subjects:
Fields (mathematics)
Lower bounds
Mathematics
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We obtain a new lower bound on the size of the value set $\mathscr{V}(f)=f(\mathbb{F}_{p})$ of a sparse polynomial $f\in \mathbb{F}_{p}[X]$ over a finite field of $p$ elements when $p$ is prime. This bound is uniform with respect to the degree and depends on some natural arithmetic properties of the degrees of the monomial terms of $f$ and the number of these terms. Our result is stronger than those that can be extracted from the bounds on multiplicities of individual values in $\mathscr{V}(f)$ .
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439519000316