{"paper":{"title":"Another application of Linnik's dispersion method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"\\'Etienne Fouvry, Maksym Radziwi{\\l}{\\l}","submitted_at":"2018-12-03T05:29:18Z","abstract_excerpt":"Let $\\alpha_m$ and $\\beta_n$ be two sequences of real numbers supported on $[M, 2M]$ and $[N, 2N]$ with $M = X^{1/2 - \\delta}$ and $N = X^{1/2 + \\delta}$. We show that there exists a $\\delta_0 > 0$ such that the multiplicative convolution of $\\alpha_m$ and $\\beta_n$ has exponent of distribution $\\frac{1}{2} + \\delta-\\varepsilon$ (in a weak sense) as long as $0 \\leq \\delta < \\delta_0$, the sequence $\\beta_n$ is Siegel-Walfisz and both sequences $\\alpha_m$ and $\\beta_n$ are bounded above by divisor functions. Our result is thus a general dispersion estimate for \"narrow\" type-II sums. The proof r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00562","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"}