{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AB2CNEJ3X7EZUSSICGP2FKRTYW","short_pith_number":"pith:AB2CNEJ3","schema_version":"1.0","canonical_sha256":"007426913bbfc99a4a48119fa2aa33c5858308f07245a9d1ff1e85dd191d5929","source":{"kind":"arxiv","id":"2404.10278","version":2},"attestation_state":"computed","paper":{"title":"Exponential sums over integers without large prime divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Sary Drappeau","submitted_at":"2024-04-16T04:36:34Z","abstract_excerpt":"We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $\\nu\\ne 0$, we also obtain new bounds on exponential sums with $\\nu$-th powers of such integers. The improvement is based on exploiting more precisely the factorisation of integers without large prime divisors, along with existing Type~I and Type~II bounds. For $\\nu=1$ we use the classical bounds of Vinogradov (1937), while for $\\nu\\neq 1$ we use bounds of Vaughan (1975) as well as of Fouvry, Kowalski and Michel (2014)."},"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":"2404.10278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-16T04:36:34Z","cross_cats_sorted":[],"title_canon_sha256":"ad708435dd8492f703c4ab5860c89501c5de571a1075d753c43468c30ce2025f","abstract_canon_sha256":"fd32755642c2366979ef7216430672e6ee9c95a219508f5029d81fa76b9956a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:15.787592Z","signature_b64":"GkUIUZS9d/IZKf1/ubrM2hG+qD7/xNABTjgj7C/ibb8FmRJ7I49msuECFYxeAHVM2rRj8BIfCBp71XKLWvM+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"007426913bbfc99a4a48119fa2aa33c5858308f07245a9d1ff1e85dd191d5929","last_reissued_at":"2026-07-05T10:58:15.787056Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:15.787056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential sums over integers without large prime divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Sary Drappeau","submitted_at":"2024-04-16T04:36:34Z","abstract_excerpt":"We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $\\nu\\ne 0$, we also obtain new bounds on exponential sums with $\\nu$-th powers of such integers. The improvement is based on exploiting more precisely the factorisation of integers without large prime divisors, along with existing Type~I and Type~II bounds. For $\\nu=1$ we use the classical bounds of Vinogradov (1937), while for $\\nu\\neq 1$ we use bounds of Vaughan (1975) as well as of Fouvry, Kowalski and Michel (2014)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.10278","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.10278/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":"2404.10278","created_at":"2026-07-05T10:58:15.787113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.10278v2","created_at":"2026-07-05T10:58:15.787113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.10278","created_at":"2026-07-05T10:58:15.787113+00:00"},{"alias_kind":"pith_short_12","alias_value":"AB2CNEJ3X7EZ","created_at":"2026-07-05T10:58:15.787113+00:00"},{"alias_kind":"pith_short_16","alias_value":"AB2CNEJ3X7EZUSSI","created_at":"2026-07-05T10:58:15.787113+00:00"},{"alias_kind":"pith_short_8","alias_value":"AB2CNEJ3","created_at":"2026-07-05T10:58:15.787113+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.22192","citing_title":"Mean value theorems with smooth numbers","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW","json":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW.json","graph_json":"https://pith.science/api/pith-number/AB2CNEJ3X7EZUSSICGP2FKRTYW/graph.json","events_json":"https://pith.science/api/pith-number/AB2CNEJ3X7EZUSSICGP2FKRTYW/events.json","paper":"https://pith.science/paper/AB2CNEJ3"},"agent_actions":{"view_html":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW","download_json":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW.json","view_paper":"https://pith.science/paper/AB2CNEJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.10278&json=true","fetch_graph":"https://pith.science/api/pith-number/AB2CNEJ3X7EZUSSICGP2FKRTYW/graph.json","fetch_events":"https://pith.science/api/pith-number/AB2CNEJ3X7EZUSSICGP2FKRTYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW/action/storage_attestation","attest_author":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW/action/author_attestation","sign_citation":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW/action/citation_signature","submit_replication":"https://pith.science/pith/AB2CNEJ3X7EZUSSICGP2FKRTYW/action/replication_record"}},"created_at":"2026-07-05T10:58:15.787113+00:00","updated_at":"2026-07-05T10:58:15.787113+00:00"}