JournalsjemsVol. 18, No. 8pp. 1753–1767

Stable lattices and the diagonal group

  • Uri Shapira

    Technion - Israel Institute of Technology, Haifa, Israel
  • Barak Weiss

    Tel Aviv University, Israel
Stable lattices and the diagonal group cover
Download PDF

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.

Cite this article

Uri Shapira, Barak Weiss, Stable lattices and the diagonal group. J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1753–1767

DOI 10.4171/JEMS/628