{"paper":{"title":"Linear and quadratic uniformity of the M\\\"obius function over $\\mathbb{F}_q[t]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Pierre-Yves Bienvenu, Th\\'ai Ho\\`ang L\\^e","submitted_at":"2017-11-14T23:43:05Z","abstract_excerpt":"We examine correlations of the M\\\"obius function over $\\mathbb{F}_q[t]$ with linear or quadratic phases, that is, averages of the form \\begin{equation} \\label{eq:average} \\frac{1}{q^n}\\sum_{\\text{deg }f<n} \\mu(f)\\chi(Q(f)) \\end{equation} for an additive character $\\chi$ over $\\mathbb{F}_q$ and a polynomial $Q\\in\\mathbb{F}_q[x_0,\\ldots,x_{n-1}]$ of degree at most 2 in the coefficients $x_0,\\ldots, x_{n-1}$ of $f=\\sum_{i< n}x_i t^i$. Like in the integers, it is reasonable to expect that, due to the random-like behaviour of $\\mu$, such sums should exhibit considerable cancellation. In this paper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05358","kind":"arxiv","version":4},"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"}