{"paper":{"title":"On multiplicatively independent bases in cyclotomic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Manfred G. Madritsch, Volker Ziegler","submitted_at":"2014-08-18T12:16:53Z","abstract_excerpt":"Recently the authors showed that the algebraic integers of the form $-m+\\zeta_k$ are bases of a canonical number system of $\\mathbb{Z}[\\zeta_k]$ provided $m\\geq \\phi(k)+1$, where $\\zeta_k$ denotes a $k$-th primitive root of unity and $\\phi$ is Euler's totient function. In this paper we are interested in the questions whether two bases $-m+\\zeta_k$ and $-n+\\zeta_k$ are multiplicatively independent. We show the multiplicative independence in case that $0<|m-n|<10^6$ and $|m|,|n|> 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3991","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"}