{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:6H26F7DA5IPGXTSU2FBIV64J3L","short_pith_number":"pith:6H26F7DA","schema_version":"1.0","canonical_sha256":"f1f5e2fc60ea1e6bce54d1428afb89dae9bf449611dbfe77bad022736fef14e6","source":{"kind":"arxiv","id":"0908.1240","version":2},"attestation_state":"computed","paper":{"title":"L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Rojas-Leon, C. Douglas Haessig","submitted_at":"2009-08-09T15:18:53Z","abstract_excerpt":"For \\psi a nontrivial additive character on the finite field F_q, the map t \\mapsto \\sum_{x \\in F_q} \\psi(f(x)+tx) is the Fourier transform of the map t \\mapsto \\psi(f(t))$. As is well-known, this has a cohomological interpretation, producing a continuous ell-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both ell-adic and p-adic methods. Using ell-adic techniques, we give an explicit formula for the degree of this L-function and determine the complex absolute values of its roots. Using p-adic techniques, we study"},"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":"0908.1240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-08-09T15:18:53Z","cross_cats_sorted":[],"title_canon_sha256":"1dc3bc1e5409f1e9c84c3c2ab715920e2f5fe9560edce5862fd114fcda8cd474","abstract_canon_sha256":"a4e4329a320c9b5fc47307e404f955327c7fdc5f448948ac8af6a8b5b5e21d68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:43.311651Z","signature_b64":"gq4JQ6Ak7SfgcEdyQLqZPy6C1sL7bbjmDAuGrpafHjJEcOdVHEqbxon3/iR0VlhHIzOAxmPXAb07cjDk5P/DDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1f5e2fc60ea1e6bce54d1428afb89dae9bf449611dbfe77bad022736fef14e6","last_reissued_at":"2026-05-18T04:42:43.311196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:43.311196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Rojas-Leon, C. Douglas Haessig","submitted_at":"2009-08-09T15:18:53Z","abstract_excerpt":"For \\psi a nontrivial additive character on the finite field F_q, the map t \\mapsto \\sum_{x \\in F_q} \\psi(f(x)+tx) is the Fourier transform of the map t \\mapsto \\psi(f(t))$. As is well-known, this has a cohomological interpretation, producing a continuous ell-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both ell-adic and p-adic methods. Using ell-adic techniques, we give an explicit formula for the degree of this L-function and determine the complex absolute values of its roots. Using p-adic techniques, we study"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1240","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":"0908.1240","created_at":"2026-05-18T04:42:43.311256+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.1240v2","created_at":"2026-05-18T04:42:43.311256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1240","created_at":"2026-05-18T04:42:43.311256+00:00"},{"alias_kind":"pith_short_12","alias_value":"6H26F7DA5IPG","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"6H26F7DA5IPGXTSU","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"6H26F7DA","created_at":"2026-05-18T12:25:58.837520+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/6H26F7DA5IPGXTSU2FBIV64J3L","json":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L.json","graph_json":"https://pith.science/api/pith-number/6H26F7DA5IPGXTSU2FBIV64J3L/graph.json","events_json":"https://pith.science/api/pith-number/6H26F7DA5IPGXTSU2FBIV64J3L/events.json","paper":"https://pith.science/paper/6H26F7DA"},"agent_actions":{"view_html":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L","download_json":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L.json","view_paper":"https://pith.science/paper/6H26F7DA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.1240&json=true","fetch_graph":"https://pith.science/api/pith-number/6H26F7DA5IPGXTSU2FBIV64J3L/graph.json","fetch_events":"https://pith.science/api/pith-number/6H26F7DA5IPGXTSU2FBIV64J3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L/action/storage_attestation","attest_author":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L/action/author_attestation","sign_citation":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L/action/citation_signature","submit_replication":"https://pith.science/pith/6H26F7DA5IPGXTSU2FBIV64J3L/action/replication_record"}},"created_at":"2026-05-18T04:42:43.311256+00:00","updated_at":"2026-05-18T04:42:43.311256+00:00"}