{"paper":{"title":"Palindromic Prefixes and Diophantine Approximation","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"St\\'ephane Fischler","submitted_at":"2005-09-22T08:38:45Z","abstract_excerpt":"This text is devoted to simultaneous approximation to $\\xi$ and $\\xi^2$ by rational numbers with the same denominator, where $\\xi$ is a non-quadratic real number. We focus on an exponent $\\beta_0(\\xi)$ that measures the quality of such approximations (when they are exceptionally good). We prove that $\\beta_0$ takes the same set of values as a combinatorial quantity that measures the abundance of palindrome prefixes in an infinite word $w$. This allows us to give a precise exposition of Roy's palindrome prefix method. The main tools we use are Davenport-Schmidt's sequence of minimal points and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509508","kind":"arxiv","version":3},"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"}