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At the end we shall prove the following long standing conjecture: for every positive integer n $$\\zeta(\\{3\\}^n)=8^n\\zeta(\\{\\ol2,1\\}^n).$$ The main idea is to use the double shuffle relations and the dist"},"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":"0705.2267","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-05-16T01:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"15567acdb72d58411f85b9e4e68c399f297b77e0f041671fdc3037eeceea3a53","abstract_canon_sha256":"e88b0c79a15ef35f8f3515bc35cb1667b1e2258a112cdbe72dd407ae7af75433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:14.783928Z","signature_b64":"V644YtMjeQfaD4TZh9hNm4Wz5GRhyWzii/5lLKwP52rpb8Jas4eny/lQz7GSQtAWROoyNUfe7cTb+8yAhlDeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c157f5335214389f97568adfe065f6f7e08da70886f0e6b6e016748db2e3c72","last_reissued_at":"2026-05-18T04:42:14.783424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:14.783424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double Shuffle Relations of Euler Sums","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jianqiang Zhao","submitted_at":"2007-05-16T01:52:09Z","abstract_excerpt":"In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, \\emph{Derivation and double shuffle relations for multiple zeta values}. 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