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).
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