{"paper":{"title":"The distribution of values of short hybrid exponential sums on curves over finite fields II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kit-Ho Mak","submitted_at":"2014-08-06T11:02:54Z","abstract_excerpt":"Let $p$ be a prime number, $C$ be any absolutely irreducible affine plane curve over $\\mathbb{F}_p$, and $g,f\\in\\mathbb{F}_p(x,y)$ be rational functions. We continue the study of the distribution of the values of short hybrid exponential sums of the form $S_{H}(x;C) = \\sum_{P\\in C, x<x(P)\\leq x+H}\\chi(g(P))\\psi(f(P))$ on $x\\in\\mathcal{I}$ for some short interval $\\mathcal{I}$. We show that under some natural conditions, the limiting distribution of the sum $S_{H}(x;C)$ is Gaussian for all curve $C$. This largely generalizes a previous result of the author and Zaharescu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1244","kind":"arxiv","version":1},"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"}