On primitive elements in finite fields of low characteristic
Number Theory
2014-12-24 v1 Computational Complexity
Abstract
We discuss the problem of constructing a small subset of a finite field containing primitive elements of the field. Given a finite field, , small and large , we show that the set of all low degree polynomials contains the expected number of primitive elements. The main theorem we prove is a bound for character sums over short intervals in function fields. Our result is unconditional and slightly better than what is known (conditionally under GRH) in the integer case and might be of independent interest.
Cite
@article{arxiv.1412.7373,
title = {On primitive elements in finite fields of low characteristic},
author = {Abhishek Bhowmick and Thái Hoàng Lê},
journal= {arXiv preprint arXiv:1412.7373},
year = {2014}
}