Linear relations with conjugates of a Salem number

Artūras Dubickas; Jonas Jankauskas

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arXiv · 1905.04023

Linear relations with conjugates of a Salem number

Artūras Dubickas·Jonas Jankauskas

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Abstract

In this paper we consider linear relations with conjugates of a Salem number $\alpha$. We show that every such a relation arises from a linear relation between conjugates of the corresponding totally real algebraic integer $\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem number with a nontrivial relation between its conjugates is $8$, whereas the smallest length of a nontrivial linear relation between the conjugates of a Salem number is $6$.

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Artūras Dubickas, Jonas Jankauskas. 2019-05-10. Linear relations with conjugates of a Salem number. https://arxiv.org/abs/1905.04023

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