Linear relations with conjugates of a Salem number

2019/05/10 by Dubickas, Artūras, Jankauskas, Jonas · 1 citation
#11R06 #11R09 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.04023

Abstract

In this paper we consider linear relations with conjugates of a Salem number α. We show that every such a relation arises from a linear relation between conjugates of the corresponding totally real algebraic integer α+1/α. 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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