Stable lattices and the diagonal group

Uri Shapira, Barak Weiss

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Inspired by work of McMullen, we show that any orbit of the diagonal group in the space of lattices accumulates on the set of stable lattices. As consequences, we settle a conjecture of Ramharter concerning the asymptotic behavior of the Mordell constant, and reduce Minkowski's conjecture on products of linear forms to a geometric question, yielding two new proofs of the conjecture in dimensions up to 7.

Original languageEnglish
Pages (from-to)1753-1767
Number of pages15
JournalJournal of the European Mathematical Society
Volume18
Issue number8
DOIs
StatePublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Diagonal group
  • Lattices
  • Stable

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