{"paper":{"title":"Major arcs for Goldbach's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"H. A. Helfgott","submitted_at":"2013-05-13T19:21:02Z","abstract_excerpt":"The ternary Goldbach conjecture states that every odd number $n\\geq 7$ is the sum of three primes. The estimation of the Fourier series $\\sum_{p\\leq x} e(\\alpha p)$ and related sums has been central to the study of the problem since Hardy and Littlewood (1923). Here we show how to estimate such Fourier series for $\\alpha$ in the so-called major arcs, i.e., for $\\alpha$ close to a rational of small denominator. This is part of the author's proof of the ternary Goldbach conjecture. In contrast to most previous work on the subject, we will rely on a finite verification of the Generalized Riemann "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2897","kind":"arxiv","version":4},"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"}