{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NBCRH6WG7LXRXKL2CLEATVNL2V","short_pith_number":"pith:NBCRH6WG","schema_version":"1.0","canonical_sha256":"684513fac6faef1ba97a12c809d5abd54323a926c18e8a891883387de7967ddb","source":{"kind":"arxiv","id":"1908.03044","version":1},"attestation_state":"computed","paper":{"title":"On Euler-Kronecker constants and the generalized Brauer-Siegel conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup B. Dixit","submitted_at":"2019-08-08T12:54:44Z","abstract_excerpt":"As a natural generalization of the Euler-Mascheroni constant $\\gamma$, Y. Ihara introduced the Euler-Kronecker constant $\\gamma_K$ attached to any number field $K$. In this paper, we prove that a certain bound on $\\gamma_K$ in a tower of number fields $\\mathcal{K}$ implies the generalized Brauer-Siegel conjecture for $\\mathcal{K}$ as formulated by Tsfasman and Vl\\v{a}du\\c{t}. Moreover, we use known bounds on $\\gamma_K$ for cyclotomic fields to obtain a finer estimate for the number of zeros of the Dedekind zeta-function $\\zeta_K(s)$ in the critical strip."},"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":"1908.03044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-08T12:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"1720b3d1605205d690251c932127697dff0ef047037b89608d5a36eeeffdc624","abstract_canon_sha256":"1ae26b63178302921ad18b27c4db699c22f52868852fd1881c48b5a2936e6dba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:25.705565Z","signature_b64":"nC/EOBeuLcwC7/x01nlEfuG5gLuRFOmqchvDLhk6Cvp3y4CziVTu2hZU3FE9FxMNmqOWeoA/UJ0223dArjOZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"684513fac6faef1ba97a12c809d5abd54323a926c18e8a891883387de7967ddb","last_reissued_at":"2026-07-04T23:52:25.705081Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:25.705081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Euler-Kronecker constants and the generalized Brauer-Siegel conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup B. Dixit","submitted_at":"2019-08-08T12:54:44Z","abstract_excerpt":"As a natural generalization of the Euler-Mascheroni constant $\\gamma$, Y. Ihara introduced the Euler-Kronecker constant $\\gamma_K$ attached to any number field $K$. In this paper, we prove that a certain bound on $\\gamma_K$ in a tower of number fields $\\mathcal{K}$ implies the generalized Brauer-Siegel conjecture for $\\mathcal{K}$ as formulated by Tsfasman and Vl\\v{a}du\\c{t}. Moreover, we use known bounds on $\\gamma_K$ for cyclotomic fields to obtain a finer estimate for the number of zeros of the Dedekind zeta-function $\\zeta_K(s)$ in the critical strip."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03044","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/1908.03044/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":"1908.03044","created_at":"2026-07-04T23:52:25.705146+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03044v1","created_at":"2026-07-04T23:52:25.705146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03044","created_at":"2026-07-04T23:52:25.705146+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBCRH6WG7LXR","created_at":"2026-07-04T23:52:25.705146+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBCRH6WG7LXRXKL2","created_at":"2026-07-04T23:52:25.705146+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBCRH6WG","created_at":"2026-07-04T23:52:25.705146+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/NBCRH6WG7LXRXKL2CLEATVNL2V","json":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V.json","graph_json":"https://pith.science/api/pith-number/NBCRH6WG7LXRXKL2CLEATVNL2V/graph.json","events_json":"https://pith.science/api/pith-number/NBCRH6WG7LXRXKL2CLEATVNL2V/events.json","paper":"https://pith.science/paper/NBCRH6WG"},"agent_actions":{"view_html":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V","download_json":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V.json","view_paper":"https://pith.science/paper/NBCRH6WG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03044&json=true","fetch_graph":"https://pith.science/api/pith-number/NBCRH6WG7LXRXKL2CLEATVNL2V/graph.json","fetch_events":"https://pith.science/api/pith-number/NBCRH6WG7LXRXKL2CLEATVNL2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V/action/storage_attestation","attest_author":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V/action/author_attestation","sign_citation":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V/action/citation_signature","submit_replication":"https://pith.science/pith/NBCRH6WG7LXRXKL2CLEATVNL2V/action/replication_record"}},"created_at":"2026-07-04T23:52:25.705146+00:00","updated_at":"2026-07-04T23:52:25.705146+00:00"}