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 over a finite field . We obtain the exact probability distribution and show that the number of missing values tends to a normal distribution as goes to infinity. We obtain these results through a study of a random -th order cyclotomic mappings. A variation on the size of the union of some random sets is also considered.
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}
}