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Recently Shen and Cai gave formulas for T(2n,d) for d<6 in terms of t(2n), t(2)t(2n-2) and t(4)t(2n-4). In this short note we generalize Shen-Cai's results to arbitrary depth by using the theory of symmetric functions established by Hoffman."},"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":"1207.2368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T14:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"540962991e438a8947a0cd8b46d84f99c8e5c8ace07628ea93c5dffed61d50bf","abstract_canon_sha256":"dba6b760cc2efa9f4db7fd20518f282fa1b2f61ad215d0f508573c7569b7f6a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:14.753899Z","signature_b64":"+HIsb1AQAMAep0C6amANkhKUBUYoOUymkXSjsXSaytE6Aye9rOLH+B1gWgHvfDAmH5yXkH+WsPo1yt9WJsywBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0db7e0b0b9e551797daa2f6ba0308f7020ba72bab667de9be218911f1d814bda","last_reissued_at":"2026-05-18T00:19:14.753133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:14.753133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum Formula of Multiple Hurwitz-Zeta Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jianqiang Zhao","submitted_at":"2012-07-10T14:30:25Z","abstract_excerpt":"Let s_1,...,s_d be d positive integers and consider the multiple Hurwitz-zeta value zeta(s_1,...,s_d;-1/2,...,-1/2)/2^w where w=s_1+...+s_d is called the weight. For d<n+1, let T(2n,d) be the sum of all these values with even arguments whose weight is 2n and whose depth is d. Recently Shen and Cai gave formulas for T(2n,d) for d<6 in terms of t(2n), t(2)t(2n-2) and t(4)t(2n-4). In this short note we generalize Shen-Cai's results to arbitrary depth by using the theory of symmetric functions established by Hoffman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2368","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.2368","created_at":"2026-05-18T00:19:14.753273+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2368v1","created_at":"2026-05-18T00:19:14.753273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2368","created_at":"2026-05-18T00:19:14.753273+00:00"},{"alias_kind":"pith_short_12","alias_value":"BW36BMFZ4VIX","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BW36BMFZ4VIXS7NK","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BW36BMFZ","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA","json":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA.json","graph_json":"https://pith.science/api/pith-number/BW36BMFZ4VIXS7NKF5V2AMEPOA/graph.json","events_json":"https://pith.science/api/pith-number/BW36BMFZ4VIXS7NKF5V2AMEPOA/events.json","paper":"https://pith.science/paper/BW36BMFZ"},"agent_actions":{"view_html":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA","download_json":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA.json","view_paper":"https://pith.science/paper/BW36BMFZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2368&json=true","fetch_graph":"https://pith.science/api/pith-number/BW36BMFZ4VIXS7NKF5V2AMEPOA/graph.json","fetch_events":"https://pith.science/api/pith-number/BW36BMFZ4VIXS7NKF5V2AMEPOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA/action/storage_attestation","attest_author":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA/action/author_attestation","sign_citation":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA/action/citation_signature","submit_replication":"https://pith.science/pith/BW36BMFZ4VIXS7NKF5V2AMEPOA/action/replication_record"}},"created_at":"2026-05-18T00:19:14.753273+00:00","updated_at":"2026-05-18T00:19:14.753273+00:00"}