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

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 $Y^n + λ_{n-1}Y^{n-1} + \ldots+λ_1Y + λ_0 \in \mathbb{F}_q[X][Y ]$ where $n \geq2, λ_0\neq 0$ and $°λ_{n-1} < °λ_{n-2} = \max_{i\neq n-2}°(λ_i)$. This work provides an analogue of their results for 2-Salem elements whose minimal polynomials meet certain requirements.

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