{"paper":{"title":"Analogues of Lehmer's conjecture in positive characteristic","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Amilcar Pacheco","submitted_at":"2000-11-15T19:19:30Z","abstract_excerpt":"Let $C$ be a smooth projective irreducible curve defined over a finite field $\\mathbb{F}_q$ and $K=\\mathbb{F}_q(C)$. Let $A\\subset K$ be the ring of functions regular outside a fixed place $\\infty$ of $K$. Let $\\phi:A\\to\\text{End}(\\mathbb{G}_a)$ be a Drinfeld $A$-module of rank $r$ defined over a finite extension $L$ of $K$ and $\\hat{h}_{\\phi}$ its canonical height. Given a non-torsion point $\\alpha$ of $\\phi$ of degree $d$ over $K$, we prove that $\\hat{h}_{\\phi}(\\alpha)\\ge 1/d$.\n A similar statement is proved for the canonical height of a point of infinite order of a non-constant semi-stable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011102","kind":"arxiv","version":6},"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"}