28 citations · 42 across the 21 of their papers we have counts for
25 papers
On triviality of uniform Diophantine exponents of lattices
Oleg N. German
In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values.
An analogue of Mahler's transference theorem for multiplicative Diophantine approximation
Oleg N. German
Khintchine's and Dyson's transference theorems can be very easily deduced from Mahler's transference theorem. In the multiplicative setting an obstacle appears, which does not allo…
Geometry of Diophantine exponents
Oleg N. German
Diophantine exponents are ones of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is ai…
Diophantine exponents of lattices and growth of multidimensional analogues of partial quotients
Elmir R. Bigushev, Oleg N. German
In this paper we study the three-dimensional analogue of the relation between the irrationality exponent of a real number and the growth of its regular continued fraction partial q…
Symmetries of a two-dimensional continued fraction
Oleg N. German, Ibragim A. Tlyustangelov
In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra.…
Multiparametric geometry of numbers and its application to splitting transference theorems
Oleg N. German
In this paper we consider a multiparametric version of Wolfgang Schmidt and Leonard Summerer's parametric geometry of numbers. We apply this approach in two settings: the first one…