{"paper":{"title":"Linear relations with conjugates of a Salem number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Art\\=uras Dubickas, Jonas Jankauskas","submitted_at":"2019-05-10T09:16:22Z","abstract_excerpt":"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 $6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04023","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}