{"paper":{"title":"$p$-adic $L$-functions for elliptic curves over global function fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ki-Seng Tan","submitted_at":"2026-03-11T09:28:06Z","abstract_excerpt":"We introduce a $p$-adic $L$-function $\\mathscr L_{A/L}$ associated to an ordinary elliptic curve $A$ over a global function field $K$ of characteristic $p$ together with a $\\mathbb{Z}_{p}^{d}$-extension $L/K$, $d=0$ allowed, unramified outside a finite set of places where $A$ has ordinary (good ordinary or multiplicative) reductions. This $\\mathscr L_{A/L}$ is characterized by its interpolation of the special values of twisted Hasse-Weil $L$-functions, we show that it satisfies the desired functional equation and specialization formula in connection with the characteristic ideal of the dual $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.10576","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/2603.10576/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"}