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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 $6$.
$\alpha$. 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 language | English |
|---|---|
| Pages (from-to) | 179–191 |
| Number of pages | 13 |
| Journal | Journal de théorie des nombres de Bordeaux |
| Volume | 32 |
| Publication status | Published - 2020 |
Keywords
- Additive linear relations
- Salem numbers
- Pisot numbers
- Totally real algebraic numbers
Activities
- 1 Hosting an academic visitor
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Artūras Dubickas
Jonas Jankauskas (Host)
23 Apr 2019 → 28 Apr 2019Activity: Hosting a visitor › Hosting an academic visitor