{"paper":{"title":"$L^p$ norms of the lattice point discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Bianca Gariboldi, Giacomo Gigante, Leonardo Colzani","submitted_at":"2018-05-03T14:41:26Z","abstract_excerpt":"We estimate the $L^{p}$ 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 $\\mathbb{R}^{d}$ with smooth boundary with strictly positive curvature, \\[ \\left\\{ {\\displaystyle\\int_{\\mathbb R}}{\\displaystyle\\int_{\\mathbb{T}^{d}}}\\left\\vert \\sum_{k\\in\\mathbb{Z}^{d}}\\chi _{r\\Omega-x}(k)-r^{d}\\left\\vert \\Omega\\right\\vert \\right\\vert ^{p}dxd\\mu(r-R) \\right\\} ^{1/p}, \\] where $\\mu$ is a Borel measure compactly supported on the positive real axis and $R\\to+\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06520","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"}