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The multiple Barnes-Euler zeta function $\\zeta_{E,N}(s,x;\\bar\\omega)$ with parameter vector $\\bar\\omega=(\\omega_1,\\ldots,\\omega_N)$ is defined as a deformation of the Barnes multiple zeta function as follows $$ \\zeta_{E,N}(s,x;\\bar\\omega)=\\sum_{t_1=0}^\\infty\\cdots\\sum_{t_N=0}^\\infty \\frac{(-1)^{t_1+\\cdots+t_N}}{(x+\\omega_1t_1+\\cdots+\\omega_Nt_N)^s}. $$\n  In this paper, based on the fermionic $p$-adic integral, we define the $p$-adic analogue of multiple Barnes-Euler zeta funct"},"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":"1703.05434","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-16T00:19:48Z","cross_cats_sorted":[],"title_canon_sha256":"fcb6ec1b18b4a685ec9b8c0cfcda168d6119cb8621bdf58570b3d928b2e95b2a","abstract_canon_sha256":"10bb175b35775ac8d23b0ddccd3178cca8f74b3a1dc0aacc72c3c9ebcb91c94b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:51.390486Z","signature_b64":"3qZjDYIJsrdocbGXG7DyBoJtdvR9I6s8sfx4hVPfNhM0auU+mjDJEHQcIKcLSlQG3HQZYCJBtxOYAuECQe1HCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9f69e66dbed1ef1fc8d137bb1dc500bd535381b4b12180dfba13212302625fa","last_reissued_at":"2026-05-18T00:05:51.389857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:51.389857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $p$-adic multiple Barnes-Euler zeta functions and the corresponding log gamma functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Min-Soo Kim, Su Hu","submitted_at":"2017-03-16T00:19:48Z","abstract_excerpt":"Suppose that $\\omega_1,\\ldots,\\omega_N$ are positive real numbers and $x$ is a complex number with positive real part. The multiple Barnes-Euler zeta function $\\zeta_{E,N}(s,x;\\bar\\omega)$ with parameter vector $\\bar\\omega=(\\omega_1,\\ldots,\\omega_N)$ is defined as a deformation of the Barnes multiple zeta function as follows $$ \\zeta_{E,N}(s,x;\\bar\\omega)=\\sum_{t_1=0}^\\infty\\cdots\\sum_{t_N=0}^\\infty \\frac{(-1)^{t_1+\\cdots+t_N}}{(x+\\omega_1t_1+\\cdots+\\omega_Nt_N)^s}. $$\n  In this paper, based on the fermionic $p$-adic integral, we define the $p$-adic analogue of multiple Barnes-Euler zeta funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05434","kind":"arxiv","version":4},"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":"1703.05434","created_at":"2026-05-18T00:05:51.389933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.05434v4","created_at":"2026-05-18T00:05:51.389933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05434","created_at":"2026-05-18T00:05:51.389933+00:00"},{"alias_kind":"pith_short_12","alias_value":"VH3J4ZW35UPP","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VH3J4ZW35UPPD7EN","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VH3J4ZW3","created_at":"2026-05-18T12:31:49.984773+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/VH3J4ZW35UPPD7ENCN53DXCQBP","json":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP.json","graph_json":"https://pith.science/api/pith-number/VH3J4ZW35UPPD7ENCN53DXCQBP/graph.json","events_json":"https://pith.science/api/pith-number/VH3J4ZW35UPPD7ENCN53DXCQBP/events.json","paper":"https://pith.science/paper/VH3J4ZW3"},"agent_actions":{"view_html":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP","download_json":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP.json","view_paper":"https://pith.science/paper/VH3J4ZW3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.05434&json=true","fetch_graph":"https://pith.science/api/pith-number/VH3J4ZW35UPPD7ENCN53DXCQBP/graph.json","fetch_events":"https://pith.science/api/pith-number/VH3J4ZW35UPPD7ENCN53DXCQBP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP/action/storage_attestation","attest_author":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP/action/author_attestation","sign_citation":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP/action/citation_signature","submit_replication":"https://pith.science/pith/VH3J4ZW35UPPD7ENCN53DXCQBP/action/replication_record"}},"created_at":"2026-05-18T00:05:51.389933+00:00","updated_at":"2026-05-18T00:05:51.389933+00:00"}