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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 $\\zeta^{\\prime}(0)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.22421","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:42:20Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1f6370061095b28428cc7582a589e8cc41f5755a19f556407a90644278bab09a","abstract_canon_sha256":"6ef686e4f8e454ce9c388e14c0565fc7cf19a48712374a6ea4d267ae7d11eb56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:42.433835Z","signature_b64":"GX5aI9nQSASdfJJ86wa4u4A2TrUF+laUXSmd2XTa0YsZqElwB6atrfn0FvpYpafFL30tgisNU3XHlPizg3IPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3a5b9ae890d24bbb510f95454bc18dab65a01ab2405798541f4f1afc2aec52b","last_reissued_at":"2026-05-22T01:04:42.433207Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:42.433207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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