Linear relations with conjugates of a Salem number

Artūras Dubickas, Jonas Jankauskas

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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 $6$.
Original languageEnglish
Pages (from-to)179–191
Number of pages13
JournalJournal de théorie des nombres de Bordeaux
Issue number1
Publication statusPublished - 2020


  • Additive linear relations
  • Salem numbers
  • Pisot numbers
  • Totally real algebraic numbers

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