Category: Geometry of numbers

Ehrhart's volume conjecture
In the geometry of numbers, Ehrhart's volume conjecture gives an upper bound on the volume of a convex body containing only one lattice point in its interior. It is a kind of converse to Minkowski's t
Minkowski's second theorem
In mathematics, Minkowski's second theorem is a result in the geometry of numbers about the values taken by a norm on a lattice and the volume of its fundamental cell.
The Geometry of Numbers
The Geometry of Numbers is a book on the geometry of numbers, an area of mathematics in which the geometry of lattices, repeating sets of points in the plane or higher dimensions, is used to derive re
Minkowski–Hlawka theorem
In mathematics, the Minkowski–Hlawka theorem is a result on the lattice packing of hyperspheres in dimension n > 1. It states that there is a lattice in Euclidean space of dimension n, such that the c
Blichfeldt's theorem
Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area , it can be translated so that it includes at least point
Geometry of numbers
Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattic
Hermite constant
In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant γn for integers n > 0 is defined as follows. For
Mahler's compactness theorem
In mathematics, Mahler's compactness theorem, proved by Kurt Mahler, is a foundational result on lattices in Euclidean space, characterising sets of lattices that are 'bounded' in a certain definite s
Schinzel's theorem
In the geometry of numbers, Schinzel's theorem is the following statement: Schinzel's theorem — For any given positive integer , there exists a circle in the Euclidean plane that passes through exactl
Klein polyhedron
In the geometry of numbers, the Klein polyhedron, named after Felix Klein, is used to generalize the concept of continued fractions to higher dimensions.
Minkowski's theorem
In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning