Lattice points close to the Heisenberg spheres
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Publication:2691629
DOI10.1007/s44007-022-00040-zOpenAlexW4321481956MaRDI QIDQ2691629
Elizabeth G. Campolongo, Krystal Taylor
Publication date: 29 March 2023
Published in: La Matematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.02163
lattice pointsgeometric sumsenergy integralsGauss circle problemlink between geometric measure theory and number theory
Asymptotic results on arithmetic functions (11N37) Lattices and convex bodies (number-theoretic aspects) (11H06) Length, area, volume, other geometric measure theory (28A75) Lattice points in specified regions (11P21)
Cites Work
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- Finite chains inside thin subsets of \(\mathbb{R}^d\)
- Lattice points close to families of surfaces, nonisotropic dilations and regularity of generalized Radon transforms
- The lattice discrepancy of bodies bounded by a rotating Lamé's curve
- Geometric properties of Heisenberg-type groups
- Integer points on hypersurfaces
- The local contribution of zeros of curvature to lattice point asymptotics
- Lattice points in convex bodies with planar points on the boundary
- Lattice points in three-dimensional convex bodies with points of Gaussian curvature zero at the boundary
- On the lattice discrepancy of bodies of rotation with boundary points of curvature zero
- Über Integrale auf konvexen Körpern. I, II
- Integer points close to convex hypersurfaces
- On the Hausdorff dimensions of distance sets
- On the Number of Lattice Points in a Convex Set
- Subadditivity of Homogeneous Norms on Certain Nilpotent Lie Groups
- Harmonic Analysis in Phase Space. (AM-122)
- Wiener's test for the Brownian motion on the Heisenberg group
- Lattice points in bodies of revolution
- Exponential Sums and Lattice Points III
- The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved
- Decoupling for Perturbed Cones and the Mean Square of $|\zeta (\frac 12+it)|$
- On an analogue of the Gauss circle problem for the Heisenberg group
- Fourier Analysis and Hausdorff Dimension
- A Lattice-Point Problem
- Fourier transforms of surface-carried measures and differentiability of surface averages
- A Lattice-Point Problem. II
- A Lower Bound for the Volume of Strictly Convex Bodies with many Boundary Lattice Points
- Lebesgue Space Estimates for Spherical Maximal Functions on Heisenberg Groups
- The lattice point counting problem on the Heisenberg groups
