{"paper":{"title":"A quick distributional way to reproduce some results of the Riemann zeta function","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Hao Zhang, Junfa Deng, Yunyun Yang","submitted_at":"2026-05-21T12:42:20Z","abstract_excerpt":"The evaluation of the Riemann zeta function at negative integers is a classical result typically obtained through analytic continuation or contour integration. In this paper, we present a novel and concise derivation of these special values by employing the theory of Ces\\`aro limit of distributions, a generalized limit concept developed by Estrada, Kanwal, and Fulling. We use this tool to give a quick proof of the result that \\[ \\zeta(-n)=-\\frac{B_{n+1}}{n+1}, \\] for $n\\in\\mathbb{N}^+.$ We also give a short discussion on $\\zeta^{\\prime }(\\alpha)$ and compute the value of $\\zeta^{\\prime}(0)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22421","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/2605.22421/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"}