{"paper":{"title":"Meromorphic Continuation Of Global Zeta Function For Number Fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Subham De","submitted_at":"2023-07-22T07:38:22Z","abstract_excerpt":"In the paper, we shall establish the existence of a meromorphic continuation of the Global Zeta Function $\\zeta(f,\\chi)$ of a Global Number Field $K$ and also deduce the functional equation for the same, using different properties of the id\\`ele class group $\\mathcal{C}_K^1$ of a global field $K$ extensively defined using basic notions of Ad\\`eles ($\\mathbb{A}_{K}$) and Id\\`eles ($\\mathbb{I}_{K}$) of $K$, and also evaluating Fourier Transforms of functions $f$ on the space $\\mathcal{S}(\\mathbb{A}_{K})$ of Ad\\`elic Schwartz-Bruhat Functions. A brief overview of most of the concepts required to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12007","kind":"arxiv","version":3},"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/2307.12007/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"}