{"paper":{"title":"Mixed $L^p(L^2)$ norms of the lattice point discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NT","authors_text":"Bianca Gariboldi, Giacomo Gigante, Leonardo Colzani","submitted_at":"2017-06-14T11:47:44Z","abstract_excerpt":"We estimate some mixed $L^{p}\\left( L^{2}\\right) $ norms of the discrepancy between the volume and the number of integer points in $r\\Omega-x$, a dilated by a factor $r$ and translated by a vector $x$ of a convex body $\\Omega$ in $\\mathbb{R}^{d}$, $ \\left\\{ {\\int_{\\mathbb{T}^{d}}}\\left( \\frac{1}{H} {\\int_{R}^{R+H}}\\left\\vert \\sum_{k\\in\\mathbb{Z}^{d}}\\chi _{r\\Omega-x}(k)-r^{d}\\left\\vert \\Omega\\right\\vert \\right\\vert^{2}dr\\right)^{p/2}dx\\right\\} ^{1/p}. $ We obtain estimates for fixed values of $H$ and $R\\to\\infty$, and also asymptotic estimates when $H\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04419","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"}