{"paper":{"title":"Improved lower bounds for the Mahler measure of the Fekete polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tam\\'as Erd\\'elyi","submitted_at":"2017-02-20T00:57:27Z","abstract_excerpt":"We show that there is an absolute constant $c > 1/2$ such that the Mahler measure of the Fekete polynomials $f_p$ of the form $$f_p(z) := \\sum_{k=1}^{p-1}{\\left( \\frac kp \\right)z^k}\\,,$$ (where the coefficients are the usual Legendre symbols) is at least $c\\sqrt{p}$ for all sufficiently large primes $p$. This improves the lower bound $\\left(\\frac 12 - \\varepsilon\\right)\\sqrt{p}$ known before for the Mahler measure of the Fekete polynomials $f_p$ for all sufficiently large primes $p \\geq c_{\\varepsilon}$. Our approach is based on the study of the zeros of the Fekete polynomials on the unit cir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05827","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"}