{"paper":{"title":"Average norms of polynomials","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"T. Mansour","submitted_at":"2002-12-26T15:48:43Z","abstract_excerpt":"In this paper we study the average $\\NL_{2\\alpha}$-norm over $T$-polynomials, where $\\alpha$ is a positive integer. More precisely, we present an explicit formula for the average $\\NL_{2\\alpha}$-norm over all the polynomials of degree exactly $n$ with coefficients in $T$, where $T$ is a finite set of complex numbers, $\\alpha$ is a positive integer, and $n\\geq0$. In particular, we give a complete answer for the cases of Littlewood polynomials and polynomials of a given height. As a consequence, we derive all the previously known results for this kind of problems, as well as many new results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212344","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"}