An explicit polynomial analogue of Romanoff's theorem

Igor E. Shparlinski; Andreas J. Weingartner

An explicit polynomial analogue of Romanoff's theorem

Number Theory 2015-11-02 v1

Authors: Igor E. Shparlinski , Andreas J. Weingartner

Abstract

Given a polynomial $g$ of positive degree over a finite field, we show that the proportion of polynomials of degree $n$ , which can be written as $h+g^k$ , where $h$ is an irreducible polynomial of degree $n$ and $k$ is a nonnegative integer, has order of magnitude $1/\deg g$ .

Keywords

polynomial analogue Romanoff's theorem finite field irreducible polynomial proportion order of magnitude

Cite

@article{arxiv.1510.08991,
  title  = {An explicit polynomial analogue of Romanoff's theorem},
  author = {Igor E. Shparlinski and Andreas J. Weingartner},
  journal= {arXiv preprint arXiv:1510.08991},
  year   = {2015}
}

Related papers

View all related →