On fully split lacunary polynomials in finite fields

Abstract

We estimate the number of possible types degree patterns of $k$-lacunary polynomials of degree $t < p$ which split completely modulo $p$. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.Comment: 8 pages. Bull. Polish Acad. Sci. Math., to appea