{"paper":{"title":"Convergence to the Mahler measure and the distribution of periodic points for algebraic Noetherian $\\mathbb{Z}^d$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Vesselin Dimitrov","submitted_at":"2016-11-15T01:13:18Z","abstract_excerpt":"For every $P \\in \\mathbb{Z}[x_1^{\\pm 1}, \\ldots, x_d^{\\pm 1}] \\setminus \\{0\\}$, and every $\\varepsilon > 0$, we prove that there are a computable function $M = M(d,\\varepsilon,\\deg{P},h(P)) < \\infty$ and a finite union $Z = Z(d,\\varepsilon,\\deg{P},h(P))$ of proper torsion cosets $\\boldsymbol{\\mu} T \\subsetneq \\mathbb{G}_m^d$ such that, for every $N \\in \\mathbb{N}$, $Z$ contains all but at most $M$ of the torsion points $\\boldsymbol{\\zeta} \\in \\mu_N^d$ satisfying $|P(\\boldsymbol{\\zeta})| < e^{-\\varepsilon \\phi(N)}$. This extends a well known structural theorem from torsion points lying exactly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04664","kind":"arxiv","version":2},"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"}