Minkowski’s Conjecture, Well-Rounded Lattices and Topological Dimension
By Curtis T. McMullen. 2005
81 citations recorded by the source corpus.
Let A C SLn(R) be the diagonal subgroup, and identify SLn(R)/SLn(Z) with the space of unimodular lattices in Rn. In this paper we show that the closure of any bounded orbit A.LcSLn(R)/SLn(Z) meets the set of well-rounded lattices. This assertion implies Minkowski's conjecture for n = 6 and yields bounds for the density of algebraic integers in totally real sextic fields. The proof is based on the theory of topological dimension, as reflected in the combinatorics of open covers of Rn and Tn.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3e358a91c35716ef3bc55e41e57fb0350c280819
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In Computational Theory and Mathematics
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Citations in the corpus
- A solution to a problem of Cassels and Diophantine properties of cubic numbers (2008, background): “ON TO A PROBLEM OF CASSELS AND DIOPHANTINE PROPERTIES OF CUBIC NUMBERS5 3. Compact A orbits The following classification theorem, essentially goes back to [Bac]. A modern proof can be found in [LW] or [Mc]. Before stating it, let us recall some notions from number theory. A totally real number field i”