{"paper":{"title":"Generalized Fourier coefficients of multiplicative functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.NT","authors_text":"Lilian Matthiesen","submitted_at":"2014-05-05T19:57:12Z","abstract_excerpt":"We introduce and analyse a general class of not necessarily bounded multiplicative functions, examples of which include the function $n \\mapsto \\delta^{\\omega (n)}$, where $\\delta \\neq 0$ and where $\\omega$ counts the number of distinct prime factors of $n$, as well as the function $n \\mapsto |\\lambda_f(n)|$, where $\\lambda_f(n)$ denotes the Fourier coefficients of a primitive holomorphic cusp form.\n  For this class of functions we show that after applying a `$W$-trick' their elements become orthogonal to polynomial nilsequences. The resulting functions therefore have small uniformity norms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1018","kind":"arxiv","version":5},"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"}