{"paper":{"title":"A class of Littlewood polynomials that are not $L^\\alpha$-flat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS","math.PR","math.SP"],"primary_cat":"math.NT","authors_text":"E. H. El Abdalaoui, M. G. Nadkarni","submitted_at":"2016-06-19T10:49:43Z","abstract_excerpt":"We exhibit a class of Littlewood polynomials that are not $L^\\alpha$-flat for any $\\alpha \\geq 0$. Indeed, it is shown that the sequence of Littlewood polynomials is not $L^\\alpha$-flat, $\\alpha \\geq 0$, when the frequency of $-1$ is not in the interval $]\\frac14,\\frac34[$. We further obtain a generalization of Jensen-Jensen-Hoholdt's result by establishing that the sequence of Littlewood polynomials is not $L^\\alpha$-flat for any $\\alpha> 2$ if the frequency of $-1$ is not $\\frac12$. Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not $L^\\alpha$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05852","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":""},"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"}