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

TL;DR

This paper extends the study of Salem elements in positive characteristic to 2-Salem elements with specific polynomial structures, providing new algebraic insights in this mathematical area.

Contribution

It generalizes previous results to 2-Salem elements with particular minimal polynomial conditions in positive characteristic fields.

Findings

Characterization of 2-Salem elements with certain polynomial forms

Extension of Salem element results to new algebraic structures

Analogue results for minimal polynomials meeting specific degree conditions

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 $Y^n + \lambda_{n-1}Y^{n-1} + \ldots+\lambda_1Y + \lambda_0 \in \mathbb{F}_q[X][Y ]$ where $n \geq2, \lambda_0\neq 0$ and $\deg \lambda_{n-1} < \deg \lambda_{n-2} = \max_{i\neq n-2}\deg(\lambda_i)$. This work provides an analogue of their results for 2-Salem elements whose minimal polynomials meet certain requirements.