Inhomogeneous extreme forms

Mathieu Dutour Sikirić; Achill Schürmann; Frank Vallentin

Displaying similar documents to “Inhomogeneous extreme forms”

On extreme forms in dimension 8

Cordian Riener (2006)

Journal de Théorie des Nombres de Bordeaux

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A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension $8$ has been completed []. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example $30$ out of the $33$ in dimension $7$ ). This is no longer the case in dimension $8$ : up to similarity,...

Almost regular quaternary quadratic forms

Jacek Bochnak, Byeong-Kweon Oh (2008)

Annales de l’institut Fourier

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We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is $p$ -anisotropic for at most one prime number $p$ . Moreover, for a prime $p$ there is an almost regular $p$ -anisotropic quaternary quadratic form if and only if $p \leq 37$ . We also study the genera containing some almost regular $p$ -anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost...

Perfect Delaunay polytopes in low dimensions.

Dutour Sikirić, Mathieu, Erdahl, Robert, Rybnikov, Konstantin (2007)

Integers

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Riemann sums over polytopes

Victor Guillemin, Shlomo Sternberg (2007)

Annales de l’institut Fourier

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It is well-known that the $N$ -th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard $O (1 / N)$ rate of convergence if the sum is over the lattice, $Z / N$ . In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.

A Bochner type theorem for inductive limits of Gelfand pairs

Marouane Rabaoui (2008)

Annales de l’institut Fourier

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In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs $(G, K)$ defined as inductive limits of increasing sequences of Gelfand pairs ${(G (n), K (n))}_{n \geq 1}$ . By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element $ϕ$ of the set $𝒫^{♮} (G)$ of $K$ -biinvariant continuous functions of positive type on $G$ .

LVMB manifolds and simplicial spheres

Jérôme Tambour (2012)

Annales de l’institut Fourier

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LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of...