English

A probabilistic approach to value sets of polynomials over finite fields

Combinatorics 2014-07-23 v1 Number Theory Probability

Abstract

In this paper we study the distribution of the size of the value set for a random polynomial with degree at most q1q-1 over a finite field Fq\mathbb{F}_q. We obtain the exact probability distribution and show that the number of missing values tends to a normal distribution as qq goes to infinity. We obtain these results through a study of a random rr-th order cyclotomic mappings. A variation on the size of the union of some random sets is also considered.

Keywords

Cite

@article{arxiv.1407.5884,
  title  = {A probabilistic approach to value sets of polynomials over finite fields},
  author = {Zhicheng Gao and Qiang Wang},
  journal= {arXiv preprint arXiv:1407.5884},
  year   = {2014}
}
R2 v1 2026-06-22T05:09:57.352Z