{"paper":{"title":"On the distribution of the number of points on a family of curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Kit-Ho Mak","submitted_at":"2011-10-21T03:11:46Z","abstract_excerpt":"Let $p$ be a large prime, $\\ell\\geq 2$ be a positive integer, $m\\geq 2$ be an integer relatively prime to $\\ell$ and $P(x)\\in\\mathbb{F}_p[x]$ be a polynomial which is not a complete $\\ell'$-th power for any $\\ell'$ for which $GCD(\\ell',\\ell)=1$. Let $\\mathcal{C}$ be the curve defined by the equation $y^{\\ell}=P(x)$, and take the points on $\\mathcal{C}$ to lie in the rectangle $[0,p-1]^2$. In this paper, we study the distribution of the number of points on $\\mathcal{C}$ inside a small rectangle among residue classes modulo $m$ when we move the rectangle around in $[0,p-1]^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4693","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"}