{"paper":{"title":"Galois orbits of torsion points over polytopes near atoral sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Chenying Lin","submitted_at":"2024-12-15T11:27:30Z","abstract_excerpt":"Given an essentially atoral Laurent polynomial $P$, we show an equidistribution theorem for the function $\\operatorname{log}|P|$ on specific subsets of Galois orbits of torsion points of the $d$-dimensional algebraic torus $\\mathbb{G}^d_m(\\overline{\\mathbb{Q}})$. The specific subsets under consideration are the preimages of $d$-dimensional polytopes within the hypercube $[0,1]^d$ under the cotropicalization map. This generalises an equidistribution theorem of V. Dimitrov and P. Habegger, who considered only all Galois orbits that correspond to the entire hypercube $[0,1]^d$. In addition, we pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11156","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11156/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}