{"paper":{"title":"Improved lower bound for the number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tam\\'as Erd\\'elyi","submitted_at":"2017-02-20T00:26:07Z","abstract_excerpt":"Let $n_1 < n_2 < \\cdots < n_N$ be non-negative integers. In a private communication Brian Conrey asked how fast the number of real zeros of the trigonometric polynomials $T_N(\\theta) = \\sum_{j=1}^N {\\cos (n_j\\theta)}$ tends to $\\infty$ as a function of $N$. Conrey's question in general does not appear to be easy.Let ${\\mathcal P}_n(S)$ be the set of all algebraic polynomials of degree at most $n$ with each of their coefficients in $S$. For a finite set $S \\subset {\\mathbb C}$ let $M = M(S) := \\max\\{|z|: z \\in S\\}$. It has been shown recently that if $S \\subset {\\mathbb R}$ is a finite set and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05823","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"}