Geodesic
Value Sets of Sparse Polynomials
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 187-196

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DOI

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 $\mathscr{V}(f)$.
DOI : 10.4153/S0008439519000316
Mots-clés : sparse polynomial, value set, rational point on curve 
Shparlinski, Igor E.; Voloch, José Felipe. Value Sets of Sparse Polynomials. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 187-196. doi: 10.4153/S0008439519000316
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     year = {2020},
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     doi = {10.4153/S0008439519000316},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000316/}
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