O -posunutiach
Odd unimodular lattices of minimum 4
On a decomposition of integer vectors, II
On a generalization of the Selection Theorem of Mahler
The set of point sets of , having the property that their minimal interpoint distance is greater than a given strictly positive constant is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset of the finite point sets is compatible with the restriction of this topology to . We show that its subsets of Delone sets of given constants in , are compact. Three (classes of) metrics, whose one of crystallographic nature,...
On a Hadwiger-Wills inequality concerning lattice points.
On a Problem Connected with a Theorem of Jarnik.
On a question of Schmidt and Summerer concerning -systems
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes to provide -systems with , for arbitrary . We visualize our constructions with graphics. We further present explicit examples of numbers that induce the -systems in question.
On a question regarding visibility of lattice points, II
On an analog of Hermite's constant.
On integer points in polygons
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the -dilatation, , of certain classes of irrational polygons the error terms are bounded as with some , or as with arbitrarily small .
On Lattice Points in Polyhedral Cross-Sections.
On lattice polytopes having interior lattice points.
On Norm Three Vectors in Integral Euclidean Lattices. I.
On systems of linear inequalities
We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
On the index of the boundary points of four-dimensional lattices that are admissible for a cube.
On the lattice point theory of multidimensional ellipsoids
On the lattice rest of a convex body in , III
On the minimum of the unit lattice
On the Number of Convex Lattice Polytopes.
On the number of lattice points inside a closed curve