A Characterisation of Leech's Lattice.
A generalization of Voronoï’s Theorem to algebraic lattices
Let be an algebraic number field and the ring of integers of . In this paper, we prove an analogue of Voronoï’s theorem for -lattices and the finiteness of the number of similar isometry classes of perfect -lattices.
A local criterion for the covering of space by convex bodies
A lower bound on packing density.
A Markoff-Type Chain for the View-Obstruction Problem for Spheres in R4.
A new sphere packing in 20 dimensions.
A non-convex generalization of the circle problem.
A note on consecutive ones in a binary matrix.
A note on palindromic delta-vectors for certain rational polytopes.
A Note on Siegel's Lemma Over Number Fields.
A note on the Hermite–Rankin constant
We generalize Poor and Yuen’s inequality to the Hermite–Rankin constant and the Bergé–Martinet constant . Moreover, we determine explicit values of some low- dimensional Hermite–Rankin and Bergé–Martinet constants by applying Rankin’s inequality and some inequalities proven by Bergé and Martinet to explicit values of , and ().
A problem of Schinzel on lattice points
A Reduction of Lattice Tiling by Translates of a Cubical Cluster.
A Remark to the Paper of H. Hadwiger "Überdeckung des Raumes durch translationsgleiche Punktmengen und Nachbarnzahl".
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A Stability Property of the Densest Circle Packing.
A theorem of Mahler and some applications to transference theorems
A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields.
A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties
A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued...
Accumulation Points of the Lagrange and Markov Spectra.