Approximation of quadratic algebraic lattices by integer lattices

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 a Prime $p$ of the form $p=2$ or $p=4k+3$.
The results of this work allow us to study questions about the best approximations of quadratic algebraic lattices by integer lattices.