{"paper":{"title":"p-adic variation of L-functions of exponential sums, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Hui June Zhu","submitted_at":"2001-11-18T01:46:25Z","abstract_excerpt":"For a polynomial $f(x)$ in $(\\mathbb{Z}_p\\cap \\mathbb{Q})[x]$ of degree $d>2$ let $L(f \\bmod p;T)$ be the $L$-function of the exponential sum of $f \\bmod p$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111194","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"}