{"paper":{"title":"The error term in the Sato-Tate theorem of Birch","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ram Murty, Neha Prabhu","submitted_at":"2019-06-08T22:18:28Z","abstract_excerpt":"We establish an error term in the Sato-Tate theorem of Birch. That is, for $p$ prime, $q=p^r$ we show that $\\#\\{ (a,b) \\in \\mathbb{F}_q^2 : \\theta_{a,b}\\in I\\} =\\mu_{ST}(I)q^2 + O_r(q^{7/4})$ for any interval $I\\subseteq[0,\\pi]$ where for an elliptic curve $E: y^2= x^3 +ax +b$, the quantity $\\theta_{a,b}$ is defined by $2\\sqrt{q}\\cos\\theta_{a,b} = q+1-E(\\mathbb{F}_q)$ and $\\mu_{ST}(I)$ denotes the Sato-Tate measure of the interval $I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03534","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"}