On the Bound of Inverse Images of a Polynomial Map

Ilya Vyugin

On the Bound of Inverse Images of a Polynomial Map

Combinatorics 2018-11-26 v1 Number Theory

Authors: Ilya Vyugin

Abstract

Let $f_1(x),\ldots,f_n(x)$ be some polynomials. The upper bound on the number of $x\in\mathbb F_p$ such that $f_1(x),\ldots,f_n(x)$ are roots of unit of order $t$ is obtained. This bound generalize the bound of the paper \cite{V-S} to the case of polynomials of degrees greater than one. The bound is obtained over fields of positive characteristic and over the complex field.

Keywords

polynomial map inverse images upper bound roots of unity finite fields positive characteristic

Cite

@article{arxiv.1811.08930,
  title  = {On the Bound of Inverse Images of a Polynomial Map},
  author = {Ilya Vyugin},
  journal= {arXiv preprint arXiv:1811.08930},
  year   = {2018}
}

Comments

10 pages

Related papers

View all related →