{"paper":{"title":"Computing the truncated theta function via Mordell integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.NT","authors_text":"Alexey Kuznetsov","submitted_at":"2013-06-18T07:04:32Z","abstract_excerpt":"Hiary [3] has presented an algorithm which allows to evaluate the truncated theta function $\\sum_{k=0}^n \\exp(2\\pi \\i (zk+\\tau k^2))$ to within $\\pm \\epsilon$ in $O(\\ln(\\tfrac{n}{\\epsilon})^{\\kappa})$ arithmetic operations for any real $z$ and $\\tau$. This remarkable result has many applications in Number Theory, in particular it is the crucial element in Hiary's algorithm for computing $\\zeta(\\tfrac{1}{2}+\\i t)$ to within $\\pm t^{-\\lambda}$ in $O_{\\lambda}(t^{\\frac{1}{3}}\\ln(t)^{\\kappa})$ arithmetic operations, see [2]. We present a significant simplification of Hiary's algorithm for evaluati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4081","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"}