{"paper":{"title":"The Carlitz module and a differential Ax-Lindemann-Weierstrass theorem for the Euler gamma function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NT","authors_text":"Federico Pellarin, Lucia Di Vizio","submitted_at":"2025-08-28T22:02:45Z","abstract_excerpt":"We prove a differential transcendence result of type \"Ax-Lindemann-Weierstrass\" for Euler's gamma function. Given meromorphic functions $\\zeta_1,\\dots,\\zeta_n$ of a complex variable $\\nu$ that are pairwise distinct modulo $\\mathbb Z$ and algebraic over the field $k$ of meromorphic $1$-periodic functions, the functions $ \\Gamma(\\nu-\\zeta_1(\\nu)),\\dots,\\Gamma(\\nu-\\zeta_n(\\nu))$ are differentially independent over the field $k(\\nu)$.\n  We determine the structure of certain difference field extensions related to the torsion of an avatar of the Carlitz module over meromorphic functions. These exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21237","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.21237/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"}