{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YEIXSAEVCPAJ5AGZ5Z3A6FVCVJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"43cbb764693741061df5b621d114db0e2e44bc5c4bfac84331e23a33a17c921e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-02T07:52:22Z","title_canon_sha256":"1bb31cacbcab8f821fb2ebca24c9b72297c1413c18a7a0b0867e68be55e56219"},"schema_version":"1.0","source":{"id":"1811.00765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00765","created_at":"2026-05-18T00:01:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00765v1","created_at":"2026-05-18T00:01:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00765","created_at":"2026-05-18T00:01:42Z"},{"alias_kind":"pith_short_12","alias_value":"YEIXSAEVCPAJ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YEIXSAEVCPAJ5AGZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YEIXSAEV","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:4ca264eebf2bfecf5603c0069f1efd9e18054ba0481a52e8dad2ba737751b649","target":"graph","created_at":"2026-05-18T00:01:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We obtain new bounds of exponential sums modulo a prime $p$ with binomials $ax^k + bx^n$. In particular, for $k=1$, we improve the bound of Karatsuba (1967) from $O(n^{1/4} p^{3/4})$ to $O\\left(p^{3/4} + n^{1/3}p^{2/3}\\right)$ for any $n$, and then use it to improve the bound of Akulinichev (1965) from $O(p^{5/6})$ to $O(p^{4/5})$ for $n | (p-1)$. The result is based on a new bound on the number of solutions and of degrees of irreducible components of certain equations over finite fields.","authors_text":"Igor E. Shparlinski, Jose Felipe Voloch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-02T07:52:22Z","title":"Binomial exponential sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00765","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:43c6a7a5ea0fb8216608a2c3c995f01deeaad91302cbfffaad07ddfd3ad8d325","target":"record","created_at":"2026-05-18T00:01:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"43cbb764693741061df5b621d114db0e2e44bc5c4bfac84331e23a33a17c921e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-02T07:52:22Z","title_canon_sha256":"1bb31cacbcab8f821fb2ebca24c9b72297c1413c18a7a0b0867e68be55e56219"},"schema_version":"1.0","source":{"id":"1811.00765","kind":"arxiv","version":1}},"canonical_sha256":"c11179009513c09e80d9ee760f16a2aa50ec019f92f1baa801d762de55756411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c11179009513c09e80d9ee760f16a2aa50ec019f92f1baa801d762de55756411","first_computed_at":"2026-05-18T00:01:42.236902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:42.236902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JtNqfhODomU2oYXx8iJYrz/40yTxKqyyik/qkqLZM2omIO4oMK4+wYQGBBdq7xumWRCuUqvlrz4J90qz5W6UBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:42.237567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c6a7a5ea0fb8216608a2c3c995f01deeaad91302cbfffaad07ddfd3ad8d325","sha256:4ca264eebf2bfecf5603c0069f1efd9e18054ba0481a52e8dad2ba737751b649"],"state_sha256":"ade034e2f06a3615e3f5fa20e5b41e9f5028852882ad6e3a556b9d8185984820"}