Minkowski's second theorem in the Geometry of Numbers provides optimal upper and lower
bounds for the volume of an o-symmetric convex body in terms of its successive minima. In …

The main result of this paper is an inequality relating the lattice point enumerator of a 3-
dimensional, 0-symmetric convex body and its successive minima. This is an example of …

Gardner et al. posed the problem to find a discrete analogue of Meyer's inequality bounding
from below the volume of a convex body by the geometric mean of the volumes of its slices …

As a discrete counterpart to the classical theorem of Fritz John on the approximation of
symmetric n-dimensional convex bodies K by ellipsoids, Tao and Vu introduced so called …

Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric
convex body K over the covolume of a lattice Λ can be bounded above by a quantity …

The famous LLL algorithm is the first polynomial time lattice reduction algorithm which is
widely used in many applications. In this paper, we present a novel weak Quasi-Jacobi …

Minkowski's second theorem on successive minima gives an upper bound on the volume of
a convex body in terms of its successive minima. We study the problem to generalize …

As a discrete counterpart to the classical John theorem on the approximation of (symmetric)
$ n $-dimensional convex bodies $ K $ by ellipsoids, Tao and Vu introduced so called …

We study problems concerning lattice points and convex bodies in Adelic Geometry of
Numbers (with respect to number fields). This theory was established by Bombieri and …

The main result of this paper is an inequality relating the lattice point enumerator of a 3-
dimensional, 0-symmetric convex body and its successive minima. This is an example of …