Salem numbers less than the plastic constant

arXiv - MATH - Number Theory Pub Date : 2024-09-17 DOI:arxiv-2409.11159

Jean-Marc Sac-Épée

引用次数: 0

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.

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小于塑性常数的塞勒姆数

在 M. Mossinghoff 的网站 (\cite{MossinghoffList})上有一个小于 1.3$ 的萨林数列表。在 \cite{MossinghoffRhinWu2008} 中，这个列表被认证为完整到 44 元的度数，而且只包括一个度数为 46 元的塞勒姆数。本研究的目的是通过扩展 \cite{MossinghoffList}列表，提供一个小于可塑常数（用$\ea$表示，约等于$1.324718$）的萨勒姆数列表，来加深对萨勒姆数的理解。使用的算法基于整数线性规划。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Number Theory

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