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Let $\\mathrm{NP}(f \\bmod p)$ denote the Newton polygon of $L(f \\bmod p;T)$. Let $\\mathrm{HP}(f)$ denote the Hodge polygon of $f$, which is the lower convex hull in the real plane of the points $(n,n(n+1)/(2d))$ for $0\\leq n\\leq d-1$. We prove that there is a Zariski dense subset $\\mathcal{U}$ defined over $\\mathbb{Q}$ in the space $\\mathbb{A}^d$ of degree-$d$ monic polynomials over $\\mathbb{Q}$ such that for all $f$ in $\\mathcal{U}(\\mathb","authors_text":"Hui June Zhu","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2001-11-18T01:46:25Z","title":"p-adic variation of L-functions of exponential sums, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111194","kind":"arxiv","version":2},"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":"sha256:9d057c801c623dec2122f415df4e0704aa57a314ddeba2d5ce883cc53643865d","target":"record","created_at":"2026-05-18T01:08:29Z","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":"a711c3a1f7cde0d12e60a3a9fdef160a78d386d66b9d1119773c10f61a9a6759","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2001-11-18T01:46:25Z","title_canon_sha256":"ae0fbb7f7d379a92a4a633204697b52174c1f5c079aef3829974afad542e21ec"},"schema_version":"1.0","source":{"id":"math/0111194","kind":"arxiv","version":2}},"canonical_sha256":"1cf1ed1f1b6cca7d384f7c671d0820029fa1de382f6886ea1bc7cba4f1751fe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cf1ed1f1b6cca7d384f7c671d0820029fa1de382f6886ea1bc7cba4f1751fe6","first_computed_at":"2026-05-18T01:08:29.370696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:29.370696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oMd/DlJnv8wqIgRlD8R55N0yQuFVea2w+9M3LjrjcHswxRjFjd7IFXobOpoBCU4c/W+SYvcdm6XZ9EMXt0mjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:29.371349Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0111194","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d057c801c623dec2122f415df4e0704aa57a314ddeba2d5ce883cc53643865d","sha256:8f3f7ba2d0f85a041a7b0f820806e6b4ebd7a4775e6920e073da8dd17aa537a1"],"state_sha256":"d1f212acf909f5b8f80844ae23873580b84bbb66fb411601c3ee25e33ce56cfc"}