{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:I2Z3MI65FQCBWYYTAA6TOFPPU3","short_pith_number":"pith:I2Z3MI65","schema_version":"1.0","canonical_sha256":"46b3b623dd2c041b6313003d3715efa6d37bd6360eda716b341cfb5d670ffda3","source":{"kind":"arxiv","id":"2411.12404","version":1},"attestation_state":"computed","paper":{"title":"On a Birch and Swinnerton-Dyer type conjecture for the Hasse-Weil-Artin $L$-functions in characteristic $p>0$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Trihan, Ki-Seng Tan, Kwok-Wing Tsoi, Wansu Kim","submitted_at":"2024-11-19T10:41:18Z","abstract_excerpt":"Given an abelian variety $A$ over a global function field $K$ of characteristic $p>0$ and an irreducible complex continuous representation $\\psi$ of the absolute Galois group of $K$, we obtain a BSD-type formula for the leading term of Hasse--Weil--Artin $L$-function for $(A,\\psi)$ at $s=1$ under certain technical hypotheses. The formula we obtain can be applied quite generally; for example, it can be applied to the $p$-part of the leading term even when $\\psi$ is weakly wildly ramified at some place under additional hypotheses.\n  Our result is the function field analogue of the work of D. Bur"},"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":"2411.12404","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-19T10:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"42f8c5ca1a073c6c67e40ab3354c9fd630ff04ccd1277923cfb3552f6a2aea87","abstract_canon_sha256":"64833ff942824589fc22b913da62043b1e5d155aa701d1189a7f46bbb5c9ca00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:21.315810Z","signature_b64":"RRfkLZU9qkBSIYCYRC1rn0GF9HNEGDB6OkLEMNLD/8OOFUNuyfcnSq6hFUPojzTZCrG5LAjYYKKmDcKT1qW7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b3b623dd2c041b6313003d3715efa6d37bd6360eda716b341cfb5d670ffda3","last_reissued_at":"2026-07-05T09:37:21.315167Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:21.315167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Birch and Swinnerton-Dyer type conjecture for the Hasse-Weil-Artin $L$-functions in characteristic $p>0$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Trihan, Ki-Seng Tan, Kwok-Wing Tsoi, Wansu Kim","submitted_at":"2024-11-19T10:41:18Z","abstract_excerpt":"Given an abelian variety $A$ over a global function field $K$ of characteristic $p>0$ and an irreducible complex continuous representation $\\psi$ of the absolute Galois group of $K$, we obtain a BSD-type formula for the leading term of Hasse--Weil--Artin $L$-function for $(A,\\psi)$ at $s=1$ under certain technical hypotheses. The formula we obtain can be applied quite generally; for example, it can be applied to the $p$-part of the leading term even when $\\psi$ is weakly wildly ramified at some place under additional hypotheses.\n  Our result is the function field analogue of the work of D. Bur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12404","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/2411.12404/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.12404","created_at":"2026-07-05T09:37:21.315247+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12404v1","created_at":"2026-07-05T09:37:21.315247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12404","created_at":"2026-07-05T09:37:21.315247+00:00"},{"alias_kind":"pith_short_12","alias_value":"I2Z3MI65FQCB","created_at":"2026-07-05T09:37:21.315247+00:00"},{"alias_kind":"pith_short_16","alias_value":"I2Z3MI65FQCBWYYT","created_at":"2026-07-05T09:37:21.315247+00:00"},{"alias_kind":"pith_short_8","alias_value":"I2Z3MI65","created_at":"2026-07-05T09:37:21.315247+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/I2Z3MI65FQCBWYYTAA6TOFPPU3","json":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3.json","graph_json":"https://pith.science/api/pith-number/I2Z3MI65FQCBWYYTAA6TOFPPU3/graph.json","events_json":"https://pith.science/api/pith-number/I2Z3MI65FQCBWYYTAA6TOFPPU3/events.json","paper":"https://pith.science/paper/I2Z3MI65"},"agent_actions":{"view_html":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3","download_json":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3.json","view_paper":"https://pith.science/paper/I2Z3MI65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12404&json=true","fetch_graph":"https://pith.science/api/pith-number/I2Z3MI65FQCBWYYTAA6TOFPPU3/graph.json","fetch_events":"https://pith.science/api/pith-number/I2Z3MI65FQCBWYYTAA6TOFPPU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3/action/storage_attestation","attest_author":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3/action/author_attestation","sign_citation":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3/action/citation_signature","submit_replication":"https://pith.science/pith/I2Z3MI65FQCBWYYTAA6TOFPPU3/action/replication_record"}},"created_at":"2026-07-05T09:37:21.315247+00:00","updated_at":"2026-07-05T09:37:21.315247+00:00"}