Stable lattices and the diagonal group

作者:Shapira Uri*; Weiss Barak
来源:Journal of the European Mathematical Society, 2016, 18(8): 1753-1767.
DOI:10.4171/JEMS/628

摘要

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.

  • 出版日期2016