{"paper":{"title":"On the optimal weight function in the Goldston-Pintz-Yildirim method for finding small gaps between consecutive primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B\\'alint Farkas, J\\'anos Pintz, Szil\\'ard R\\'ev\\'esz","submitted_at":"2013-06-10T08:19:21Z","abstract_excerpt":"We work out the optimization problem, initiated by K. Soundararajan, for the choice of the underlying polynomial P used in the construction of the weight function in the Goldston--Pintz--Yildirim method for finding small gaps between primes. First we reformulate to a maximization problem on L^2[0,1] for a self-adjoint operator T, the norm of which is then the maximal eigenvalue of T. To find eigenfunctions and eigenvalues, we derive a differential equation which can be explicitly solved. The aimed maximal value is S(k)=4/(k+ck^{1/3}), achieved by the (k-1)st integral of x^{1-k/2}J_{k-2}(a_1\\sq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2133","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"}