On the number of distinct roots of a lacunary polynomial over finite fields

TL;DR

This paper establishes new upper bounds on the number of distinct roots of lacunary polynomials over finite fields, especially those with large gaps between exponents, advancing understanding of their root structure.

Contribution

It provides novel upper bounds for the roots of lacunary polynomials with large exponent gaps over finite fields, improving previous estimates.

Findings

New upper bounds on the number of roots for lacunary polynomials.

Applicable to polynomials with large gaps between exponents.

Enhanced understanding of root distribution in finite fields.

Abstract

We obtain new upper bounds on the number of distinct roots of lacunary polynomials over finite fields. Our focus will be on polynomials for which there is a large gap between consecutive exponents in the monomial expansion.