{"paper":{"title":"An unconditional explicit bound on the error term in the Sato-Tate conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Hoey, Fernando Trejos Su\\'arez, Jonas Iskander, Steven Jin","submitted_at":"2021-08-07T20:39:18Z","abstract_excerpt":"Let $f(z) = \\sum_{n=1}^\\infty a_f(n)q^n$ be a holomorphic cuspidal newform with even integral weight $k\\geq 2$, level $N$, trivial nebentypus, and no complex multiplication (CM). For all primes $p$, we may define $\\theta_p\\in [0,\\pi]$ such that $a_f(p) = 2p^{(k-1)/2}\\cos \\theta_p$. The Sato-Tate conjecture states that the angles $\\theta_p$ are equidistributed with respect to the probability measure $\\mu_{\\textrm{ST}}(I) = \\frac{2}{\\pi}\\int_I \\sin^2 \\theta \\; d\\theta$, where $I\\subseteq [0,\\pi]$. Using recent results on the automorphy of symmetric-power $L$-functions due to Newton and Thorne, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.03520","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.03520/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}