Number of lattice points in families of homothetic domains in \(R^ n\)

DOI10.1007/BF01083133zbMath0522.10031OpenAlexW1973601675MaRDI QIDQ1055813

Alexander Varchenko

Publication date: 1983

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01083133

zbMATH Keywords

number of lattice pointslattice remainderfamilies of homothetic domains

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Lattice points in specified regions (11P21)

Related Items (21)

Spectral theory and sheaf theory. II ⋮ The Riemann-Roch theorem for complex spaces ⋮ The approximate spectral projection method ⋮ Approximation of Lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary ⋮ Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics ⋮ Unnamed Item ⋮ Average decay of Fourier transforms and integer points in polyhedra ⋮ The number of integer points in a family of anisotropically expanding domains ⋮ Eigenfunction expansions and the Pinsky phenomenon on compact manifolds ⋮ Lattice points and generalized Diophantine conditions ⋮ Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces ⋮ Randol maximal functions and the integrability of the Fourier transform of measures ⋮ Asymptotics of variance of the lattice point count ⋮ Localization and convergence of eigenfunction expansions ⋮ Pointwise Fourier inversion on tori and other compact manifolds ⋮ Lattice points in rotated convex domains ⋮ Unnamed Item ⋮ Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition ⋮ Two-term asymptotics of the spectrum of a boundary-value problem under an interior reflection of general form ⋮ Base change and the Fredholm index ⋮ Asymptotic behavior of the spectra of diffraction problems

Cites Work

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• The number of lattice points on a convex curve
• Nombre de points entiers dans une famille homothétique de domaines de ${R}$
• On the Number of Lattice Points in a Compact n-Dimensional Polyhedron
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• A Lattice-Point Problem
• A Lattice-Point Problem. II
• On the Fourier Transform of the Indicator Function of a Planar Set
• On the Asymptotic Behavior of the Fourier Transform of the Indicator Function of a Convex Set

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