Value sets of sparse polynomials
Number Theory
2020-02-19 v2
Abstract
We obtain a new lower bound on the size of value set f(F_p) of a sparse polynomial f in F_p[X] over a finite field of p elements when p is prime. This bound is uniform with respect of 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 which canted be extracted from the bounds on multiplicities of individual values in f(F_p).
Cite
@article{arxiv.1809.02708,
title = {Value sets of sparse polynomials},
author = {Igor E. Shparlinski and Jose Felipe Voloch},
journal= {arXiv preprint arXiv:1809.02708},
year = {2020}
}