Diophantine approximation and parametric geometry of numbers

• DOI: 10.1007/s00605-012-0391-z
• Publication Date: 2012-02-20T05:41:32Z
• Authors: Wolfgang M. Schmidt; Leonhard Summerer
• Keywords: Geometry of numbers; Diophantine approximation; Diophantine geometry; Convex geometry

Dirichlet’s Theorem on simultaneous approximation involves a parameter Q. It can be derived from Minkowski’s geometry of numbers involving a symmetric convex body depending on Q. Therefore it is natural to study parametric Geometry of Numbers. In turn, this will shed new light on diophantine approximation.