{"paper":{"title":"On a mixed problem in Diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bernard De Mathan (IMB), DP), Yann Bugeaud (IRMA","submitted_at":"2009-03-16T12:53:21Z","abstract_excerpt":"Let $d$ be a positive integer. Let $p$ be a prime number. Let $\\alpha$ be a real algebraic number of degree $d+1$. We establish that there exist a positive constant $c$ and infinitely many algebraic numbers $\\xi$ of degree $d$ such that $|\\alpha - \\xi| \\cdot \\min\\{|\\Norm(\\xi)|_p,1\\} < c H(\\xi)^{-d-1} (\\log 3 H(\\xi))^{-1/d}$. Here, $H(\\xi)$ and $\\Norm(\\xi)$ denote the na{\\\"\\i}ve height of $\\xi$ and its norm, respectively. This extends an earlier result of de Mathan and Teuli\\'e that deals with the case $d=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2741","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"}