4 papers
math.NT2008
Theorem on best Diophantine approximations for linear forms
Oleg N. German, Nikolay G. Moshchevitin
We prove a new quantitative result on the degeneracy of the dimension of the subspace spanned by the best Diophantine approximations for a linear form.
math.NT2008
Linear forms of a given Diophantine type
Oleg N. German, Nikolay G. Moshchevitin
We prove a result on the existence of linear forms of a given Diophantine type.
math.NT2006
On multidimensional generalization of the Lagrange theorem on continued fractions
Oleg N. German, Evgeniy L. Lakshtanov
The Lagrange theorem on continued fractions states that a number is a quadratic surd if and only if its continued fraction expansion is eventually periodic. The current paper is de…
math.NT2005
Klein polyhedra and lattices with positive norm minima
Oleg N. German
A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of . It generalizes the concept of continued fraction. In this paper facets and e…