On the weak universality theorem

Abstract

This paper is devoted to the approximation of a quadratic algebraic lattice by an integer
lattice. It calculates the distances between a quadratic algebraic lattice and an integer lattice
when they are given by the numerator and denominator of a suitable fraction to the square root
of the discriminant d — of a square-free natural number.
The results of this work allow us to study questions about the best approximations of
quadratic algebraic lattices by integer lattices.