Integer points close to convex surfaces
Integer Points on Curves and Surfaces.
Lattice point problems and distribution of values of quadratic forms.
Lattice point problems and the central limit theorem in Euclidean spaces.
Lattice Point Theory of Irrational Ellipsoids with an Arbitrary Center.
Lattice Points.
Lattice points in a circle: An improved mean-square asymptotics
Lattice Points in a Circle and Divisors in Arithmetic Progressions.
Lattice points in bodies of revolution
Lattice points in bodies with algebraic boundary
Lattice points in ellipsoids
Lattice points in elliptic paraboloids.
Lattice points in four-dimensional tetrahedra and a conjecture of Rademacher.
Lattice Points in High-Dimensional Spheres.
Lattice Points in Large Convex Bodies.
Lattice points in large convex bodies, II
Lattice Points in Lattice Polytopes.
Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary
We investigate the number of lattice points in special three-dimensional convex bodies. They are called convex bodies of pseudo revolution, because we have in one special case a body of revolution and in another case even a super sphere. These bodies have lines at the boundary, where all points have Gaussian curvature zero. We consider the influence of these points to the lattice rest in the asymptotic representation of the number of lattice points.
Lattice points in super spheres
In this article we consider the number of lattice points in -dimensional super spheres with even power . We give an asymptotic expansion of the -fold anti-derivative of for sufficiently large . From this we deduce a new estimation for the error term in the asymptotic representation of for .
Lp-bounds for spherical maximal operators on Zn.
We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a...