{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6F5SNWWQPYRUEBUVPJNQTBURZS","short_pith_number":"pith:6F5SNWWQ","schema_version":"1.0","canonical_sha256":"f17b26dad07e234206957a5b098691cc977e792b3e30e1153ddaa3b5e0b5af62","source":{"kind":"arxiv","id":"2507.08296","version":1},"attestation_state":"computed","paper":{"title":"Large value estimates for Dirichlet polynomials, and the density of zeros of Dirichlet's $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bin Chen","submitted_at":"2025-07-11T04:05:34Z","abstract_excerpt":"It is proved that \\[ \\sum_{\\chi \\bmod q}N(\\sigma , T, \\chi) \\lesssim_{\\epsilon} (qT)^{7(1-\\sigma)/3+\\epsilon}, \\] where $N(\\sigma, T, \\chi)$ denote the number of zeros $\\rho = \\beta + it$ of $L(s, \\chi)$ in the rectangle $\\sigma \\leq \\beta \\leq 1$, $|t| \\leq T$. The exponent $7/3$ improves upon Huxley's earlier exponent of $12/5$. The key innovation lies in deriving a sharp upper bound for sums involving affine transformations with GCD twists, which emerges from our application of the Guth-Maynard method. As corollaries, we obtain two new arithmetic consequences from this zero-density estimate"},"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":"2507.08296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-11T04:05:34Z","cross_cats_sorted":[],"title_canon_sha256":"df617bc587dc7bffed4081b6a52d7c2522bd45d76a5f4ee351ed14d09aafbba7","abstract_canon_sha256":"074772c6d7817e07abba0b655da6ee8f507bbde68fa2a8e4add6bcb4aceb48c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:20.984539Z","signature_b64":"23RWfe79pTx5QwsVOeNJRDaaSoCIp0WHA5IRPSQQ2ymKIl5+Srtn9VkFGwP6Sa8sNz1w3Ty22+zueOtR9DkWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f17b26dad07e234206957a5b098691cc977e792b3e30e1153ddaa3b5e0b5af62","last_reissued_at":"2026-07-05T11:35:20.984051Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:20.984051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large value estimates for Dirichlet polynomials, and the density of zeros of Dirichlet's $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bin Chen","submitted_at":"2025-07-11T04:05:34Z","abstract_excerpt":"It is proved that \\[ \\sum_{\\chi \\bmod q}N(\\sigma , T, \\chi) \\lesssim_{\\epsilon} (qT)^{7(1-\\sigma)/3+\\epsilon}, \\] where $N(\\sigma, T, \\chi)$ denote the number of zeros $\\rho = \\beta + it$ of $L(s, \\chi)$ in the rectangle $\\sigma \\leq \\beta \\leq 1$, $|t| \\leq T$. The exponent $7/3$ improves upon Huxley's earlier exponent of $12/5$. The key innovation lies in deriving a sharp upper bound for sums involving affine transformations with GCD twists, which emerges from our application of the Guth-Maynard method. As corollaries, we obtain two new arithmetic consequences from this zero-density estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08296","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/2507.08296/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":"2507.08296","created_at":"2026-07-05T11:35:20.984110+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.08296v1","created_at":"2026-07-05T11:35:20.984110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.08296","created_at":"2026-07-05T11:35:20.984110+00:00"},{"alias_kind":"pith_short_12","alias_value":"6F5SNWWQPYRU","created_at":"2026-07-05T11:35:20.984110+00:00"},{"alias_kind":"pith_short_16","alias_value":"6F5SNWWQPYRUEBUV","created_at":"2026-07-05T11:35:20.984110+00:00"},{"alias_kind":"pith_short_8","alias_value":"6F5SNWWQ","created_at":"2026-07-05T11:35:20.984110+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2507.15334","citing_title":"Refinements for primes in short arithmetic progressions","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2605.19566","citing_title":"On the Goldbach problem with restricted primes","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS","json":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS.json","graph_json":"https://pith.science/api/pith-number/6F5SNWWQPYRUEBUVPJNQTBURZS/graph.json","events_json":"https://pith.science/api/pith-number/6F5SNWWQPYRUEBUVPJNQTBURZS/events.json","paper":"https://pith.science/paper/6F5SNWWQ"},"agent_actions":{"view_html":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS","download_json":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS.json","view_paper":"https://pith.science/paper/6F5SNWWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.08296&json=true","fetch_graph":"https://pith.science/api/pith-number/6F5SNWWQPYRUEBUVPJNQTBURZS/graph.json","fetch_events":"https://pith.science/api/pith-number/6F5SNWWQPYRUEBUVPJNQTBURZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS/action/storage_attestation","attest_author":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS/action/author_attestation","sign_citation":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS/action/citation_signature","submit_replication":"https://pith.science/pith/6F5SNWWQPYRUEBUVPJNQTBURZS/action/replication_record"}},"created_at":"2026-07-05T11:35:20.984110+00:00","updated_at":"2026-07-05T11:35:20.984110+00:00"}