{"paper":{"title":"The distribution of values of short hybrid exponential sums on curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Kit-Ho Mak","submitted_at":"2013-09-06T18:35:41Z","abstract_excerpt":"Let $p$ be a prime number, $X$ be an absolutely irreducible affine plane curve over $\\mathbb{F}_p$, and $g,f\\in\\mathbb{F}_p(x,y)$. We study the distribution of the values of the hybrid exponential sums S_n on $n\\in\\mathcal{I}$ for some short interval $\\mathcal{I}$. We show that under some natural conditions the limiting distribution of the projections of the sum $S_n$, $n\\in\\mathcal{I}$ on any straight line through the origin is Gaussian as $p$ tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1726","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"}