On the lattice point theory of multidimensional ellipsoids
On the lattice rest of a convex body in , III
On the mean squared modulus of a Dirichlet L-function over a short segment of the critical line
On the mean value of a kind of zeta functions
On the number of coprime integer pairs within a circle
On the number of lattice points in certain planar segments
On the Number of Primitive Lattice Points in Plane Domains.
On the number of primitive Pythagorean triangles
On the parity of the number of lattice points in certain tetrahedra.
On the remainder in the Weyl formula for the Euclidean disk
We prove a 2-terms Weyl formula for the counting function of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate .
On the representation of integers as sums of triangular numbers.
On the sphere problem.
One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
Points entiers au voisinage d'une courbe plane de classe Cⁿ
Polar lattices from the point of view of nuclear spaces.
The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.
Primitive lattice points in a thin strip along the boundary of a large convex planar domain
Primitive lattice points in convex planar domains
Primitive lattice points in planar domains
Primitive Lattice Points in Rational Ellipses and Relates Arithmetic Functions.
Primitive lattice points inside an ellipse
Let be a positive definite binary quadratic form with arbitrary real coefficients. For large real , one may ask for the number of primitive lattice points (integer points with ) in the ellipse disc , in particular, for the remainder term in the asymptotics for . While upper bounds for depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or...
Problème du cercle et harmoniques sphériques