Linear relations with conjugates of a Salem number
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In: Journal de théorie des nombres de Bordeaux, Vol. 32.2020, No. 1, 2020, p. 179–191.
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TY - JOUR
T1 - Linear relations with conjugates of a Salem number
AU - Dubickas, Artūras
AU - Jankauskas, Jonas
PY - 2020
Y1 - 2020
N2 - 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 relationbetween conjugates of the corresponding totally real algebraic integer$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem numberwith a nontrivial relation between its conjugates is $8$, whereas the smallestlength of a nontrivial linear relation between the conjugates of a Salem numberis $6$.
AB - 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 relationbetween conjugates of the corresponding totally real algebraic integer$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem numberwith a nontrivial relation between its conjugates is $8$, whereas the smallestlength of a nontrivial linear relation between the conjugates of a Salem numberis $6$.
KW - Additive linear relations
KW - Salem numbers
KW - Pisot numbers
KW - Totally real algebraic numbers
M3 - Article
VL - 32.2020
SP - 179
EP - 191
JO - Journal de théorie des nombres de Bordeaux
JF - Journal de théorie des nombres de Bordeaux
SN - 1246-7405
IS - 1
ER -
