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Value Sets of Sparse Polynomials
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 1 / March 2020
- Published online by Cambridge University Press:
- 24 September 2019, pp. 187-196
- Print publication:
- March 2020
-
- Article
- Export citation
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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 
$\mathscr{V}(f)$.
