Salem numbers less than the plastic constant

Abstract

A list of Salem numbers less than $1.3$ is available on M. Mossinghoff's website (\cite{MossinghoffList}). This list is certified complete up to degree $44$ in \cite{MossinghoffRhinWu2008}, and it includes only one Salem number of degree $46$. The objective of the present work is to advance the understanding of Salem numbers by extending the list \cite{MossinghoffList} through the provision of a list of Salem numbers less than the plastic constant, denoted by $\eta$, which is approximately equal to $1.324718$. The algorithmic approach used is based on Integer Linear Programming.