Supertopes
Robert Erdahl, Konstantin Rybnikov
Abstract
A perfect (Delaunay) ellipsoid is an ellipsoid in n-dimensional Euclidean space that does not contain integral points in its interior, but is uniquely defined by integral points that lie on its surface. A perfect Delaunay polytope with respect to a positive quadratic form f() is a polytope with integral vertices that is circumscribed by a perfect Delaunay ellipsoid with an equation whose quadratic part is f(). This document has been corrected on January 15, 2005. Note that it represents the state of the area as of the end of 2002. For recent research on perfect Delaunay polytopes see my recent preprint, with Erdahl and Ordine, math.NT/0408122 on ArXiv.org .
Create a lesson
Related papers
An ergodic approach to equations of the form x+y=α(n)
Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín
Rogers--Ramanujan identities from the geometry of Xa=Yb
Yifeng Huang, Kenny Lau, Ken Ono
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
Jean-Marc Sac-Épée, Souad El Otmani, Armand Maul et al.
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
A problem of Yang and Chen on weighted representation functions
Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan