{"paper":{"title":"Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry Shin","submitted_at":"2026-05-21T03:18:50Z","abstract_excerpt":"Prescribed trace/norm estimates and Soto-Andrade-type sums control whole fibers or related global character sums. We prove a coset-refined trace theorem for cubic norm-one tori. Let $B/\\mathbb{F}_q$ be finite \\'etale cubic, $\\operatorname{char}\\mathbb{F}_q\\ne2,3$, and let $T_B=\\ker(\\operatorname{N}_{B/\\mathbb{F}_q}:\\operatorname{Res}_{B/\\mathbb{F}_q}\\mathbb{G}_m\\to\\mathbb{G}_m)$. For every subgroup $H\\subset T_B(\\mathbb{F}_q)$ of index $m$, every coset $gH$, every $\\gamma\\in B^\\times$, and every smooth fiber $\\operatorname{Tr}(\\gamma h)=s$, $s^3\\ne27\\operatorname{N}(\\gamma)$, we prove $N_{gH,B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21939","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/2605.21939/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"}