{"paper":{"title":"Beta-conjugates of real algebraic numbers as Puiseux expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Louis Verger-Gaugry (IF)","submitted_at":"2011-05-03T13:00:11Z","abstract_excerpt":"The beta-conjugates of a base of numeration $\\beta > 1$, $\\beta$ being a Parry number, were introduced by Boyd, in the context of the R\\'enyi-Parry dynamics of numeration system and the beta-transformation. These beta-conjugates are canonically associated with $\\beta$. Let $\\beta > 1$ be a real algebraic number. A more general definition of the beta-conjugates of $\\beta$ is introduced in terms of the Parry Upper function $f_{\\beta}(z)$ of the beta-transformation. We introduce the concept of a germ of curve at $(0,1/\\beta) \\in \\mathbb{C}^{2}$ associated with $f_{\\beta}(z)$ and the reciprocal of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0574","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"}