\(L^{p}\) norms of the lattice point discrepancy

DOI10.1007/s00041-019-09665-1zbMath1432.11069arXiv1805.06520OpenAlexW3105945515MaRDI QIDQ2003629

Leonardo Colzani, Giacomo Gigante, Bianca Gariboldi

Publication date: 9 July 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.06520

zbMATH Keywords

convex bodydiscrepancyinteger lattice

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06) Fourier series and coefficients in several variables (42B05) Irregularities of distribution, discrepancy (11K38)

Related Items (2)

Higher moments for lattice point discrepancy of convex domains and annuli ⋮ Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy

Cites Work

• Fourier transforms related to convex sets
• A fourth power discrepancy mean
• Über Integrale auf konvexen Körpern. I, II
• On singular monotonic functions whose spectrum has a given Hausdorff dimension
• Number Theory, Fourier Analysis and Geometric Discrepancy
• L^p and Weak–L^p estimates for the number of integer points in translated domains
• Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy
• ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
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