Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy

DOI10.1090/tran/7624zbMath1419.52015arXiv1706.04419OpenAlexW2626493525MaRDI QIDQ5380480

Leonardo Colzani, Giacomo Gigante, Bianca Gariboldi

Publication date: 5 June 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04419

zbMATH Keywords

lattice point discrepancy

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)

Related Items (2)

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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Average decay of Fourier transforms and integer points in polyhedra
• Fourier transforms related to convex sets
• On the distribution of the number of lattice points inside a family of convex ovals
• Sharp rate of average decay of the Fourier transform of a bounded set
• On the mean lattice point discrepancy of a convex disc
• Mean square discrepancy bounds for the number of lattice points in large convex bodies
• \(L^{p}\) norms of the lattice point discrepancy
• A fourth power discrepancy mean
• Mean lattice point discrepancy bounds. II: Convex domains in the plane
• Über Integrale auf konvexen Körpern. I, II
• Notes on Fourier analysis. XXIX. An extrapolation theorem
• On the average order of the lattice rest of a convex planar domain
• Random fluctuations of convex domains and lattice points
• The mean lattice point discrepancy
• DISCREPANCY OF A CONVEX SET WITH ZERO CURVATURE AT ONE POINT
• Number Theory, Fourier Analysis and Geometric Discrepancy
• The distribution and moments of the error term in the Dirichlet divisor problem
• Higher-Power Moments of δ(x ), E(t ) and P(x )
• Irregularities of Distribution and Average Decay of Fourier Transforms
• L^p and Weak–L^p estimates for the number of integer points in translated domains
• Convex Bodies The Brunn-MinkowskiTheory
• Mean value theorems of the theory of lattice points. 5th report
• ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
• Lattice points and generalized Diophantine conditions

This page was built for publication: Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy