{"paper":{"title":"Counting Rational Points on Danielewski and Double Danielewski Surfaces over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.NT","authors_text":"Anit Kuckian, Indranath Sengupta, Sakshi Gupta","submitted_at":"2026-05-24T02:23:47Z","abstract_excerpt":"Let $\\Fq$ be the finite field with $q$ elements. We study the number of $\\Fq$-rational points on Danielewski and double Danielewski surfaces. For Danielewski surfaces, the point count is reduced to the number of roots of $P(Z)$ over $\\Fq.$ For double Danielewski surfaces, one has to count the number of tuples $(\\be,\\g)\\in\\Fq^2$, such that $P(0,\\g)=0$, $Q(0,\\be,\\g)=0$ hold simultaneously. We compute these numbers using gcd methods, resultants, character sums, Gauss sums, and the K\\\"onig--Rados theorem. We obtain explicit formulas in several structured cases, derive general bounds, and give a Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24821","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/2605.24821/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"}