On algebraic integers which are 2-Salem elements in positive characteristic

Abstract

Bateman and Duquette have initiated the study of Salem elements in positive characteristic. This work extends their results to 2-Salem elements whose minimal polynomials are of the type $Y^n+{\lambda }_{n-1}{Y}^{n-1}+\dots +{\lambda }_{1}Y+{\lambda }_0\in {\mathbb{F}}_q[X][Y]$ where $n\ge 2,{\lambda }_0\ne 0$ and $°{\lambda }_{n-1}<°{\lambda }_{n-2}={\max }_{i\ne n-2}°({\lambda }_i)$. This work provides an analogue of their results for 2-Salem elements whose minimal polynomials meet certain requirements.