Linear relations with conjugates of a Salem number
Artūras Dubickas, Jonas Jankauskas · Journal de Théorie des Nombres de Bordeaux · 2020
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 .