{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WTWEYMQGR7YUGZHZWTG2GBRLLO","short_pith_number":"pith:WTWEYMQG","schema_version":"1.0","canonical_sha256":"b4ec4c32068ff14364f9b4cda3062b5bb1ee34e8fd53b8ff366ce91e340d2d63","source":{"kind":"arxiv","id":"1701.01493","version":2},"attestation_state":"computed","paper":{"title":"Average values of L-functions in even characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hwanyup Jung, Sunghan Bae","submitted_at":"2017-01-05T22:38:07Z","abstract_excerpt":"Let $k = \\mathbb{F}_{q}(T)$ be the rational function field over a finite field $\\mathbb{F}_{q}$, where $q$ is a power of $2$. In this paper we solve the problem of averaging the quadratic $L$-functions $L(s, \\chi_{u})$ over fundamental discriminants. Any separable quadratic extension $K$ of $k$ is of the form $K = k(x_{u})$, where $x_{u}$ is a zero of $X^2+X+u=0$ for some $u\\in k$. We characterize the family $\\mathcal I$ (resp. $\\mathcal F$, $\\mathcal F'$) of rational functions $u\\in k$ such that any separable quadratic extension $K$ of $k$ in which the infinite prime $\\infty = (1/T)$ of $k$ r"},"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":"1701.01493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-05T22:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"0919038ba30fca8410bc37c15b04cce8940da431c40ff64c5c6f4fa68b1506c7","abstract_canon_sha256":"8301043944de30a8d1aa24673796bdbbeb690760ef489bf20ec29a30c96158fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:41.821032Z","signature_b64":"dQPvkKZn+HD/hqn3ZzzLvcZ4UogVlwBTJP0ruGA0cmyVn7scZb0XI8tkFDf6r/28o3ydwl3paAy8OocfqdffBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4ec4c32068ff14364f9b4cda3062b5bb1ee34e8fd53b8ff366ce91e340d2d63","last_reissued_at":"2026-05-18T00:49:41.820507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:41.820507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average values of L-functions in even characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hwanyup Jung, Sunghan Bae","submitted_at":"2017-01-05T22:38:07Z","abstract_excerpt":"Let $k = \\mathbb{F}_{q}(T)$ be the rational function field over a finite field $\\mathbb{F}_{q}$, where $q$ is a power of $2$. In this paper we solve the problem of averaging the quadratic $L$-functions $L(s, \\chi_{u})$ over fundamental discriminants. Any separable quadratic extension $K$ of $k$ is of the form $K = k(x_{u})$, where $x_{u}$ is a zero of $X^2+X+u=0$ for some $u\\in k$. We characterize the family $\\mathcal I$ (resp. $\\mathcal F$, $\\mathcal F'$) of rational functions $u\\in k$ such that any separable quadratic extension $K$ of $k$ in which the infinite prime $\\infty = (1/T)$ of $k$ r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01493","kind":"arxiv","version":2},"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":"1701.01493","created_at":"2026-05-18T00:49:41.820569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.01493v2","created_at":"2026-05-18T00:49:41.820569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01493","created_at":"2026-05-18T00:49:41.820569+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTWEYMQGR7YU","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTWEYMQGR7YUGZHZ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTWEYMQG","created_at":"2026-05-18T12:31:53.515858+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/WTWEYMQGR7YUGZHZWTG2GBRLLO","json":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO.json","graph_json":"https://pith.science/api/pith-number/WTWEYMQGR7YUGZHZWTG2GBRLLO/graph.json","events_json":"https://pith.science/api/pith-number/WTWEYMQGR7YUGZHZWTG2GBRLLO/events.json","paper":"https://pith.science/paper/WTWEYMQG"},"agent_actions":{"view_html":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO","download_json":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO.json","view_paper":"https://pith.science/paper/WTWEYMQG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.01493&json=true","fetch_graph":"https://pith.science/api/pith-number/WTWEYMQGR7YUGZHZWTG2GBRLLO/graph.json","fetch_events":"https://pith.science/api/pith-number/WTWEYMQGR7YUGZHZWTG2GBRLLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO/action/storage_attestation","attest_author":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO/action/author_attestation","sign_citation":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO/action/citation_signature","submit_replication":"https://pith.science/pith/WTWEYMQGR7YUGZHZWTG2GBRLLO/action/replication_record"}},"created_at":"2026-05-18T00:49:41.820569+00:00","updated_at":"2026-05-18T00:49:41.820569+00:00"}