There are Salem Numbers with Trace –3 and Every Degree At Least 34

IF 0.7 4区数学 Q2 MATHEMATICS Experimental Mathematics Pub Date : 2024-04-14 DOI:10.1080/10586458.2024.2337223

Giacomo Cherubini, Pavlo Yatsyna

引用次数: 0

Abstract

We prove that there exist Salem numbers with trace –3 and every even degree ≥34. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical...

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有轨迹为 -3 且每个度数至少为 34 的撒冷数

我们证明，存在迹为-3 且每个偶数度数≥34 的萨林数。我们的证明结合了理论方法和数值方法，理论方法允许我们处理所有足够大的度数。

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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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.

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