English

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).

Keywords

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}
}
R2 v1 2026-06-23T03:58:37.610Z