Stable lattices and the diagonal group

Uri Shapira; Barak Weiss

doi:10.4171/JEMS/628

Stable lattices and the diagonal group

Uri Shapira, Barak Weiss

Research output: Contribution to journal › Article › peer-review

15 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 language	English
Pages (from-to)	1753-1767
Number of pages	15
Journal	Journal of the European Mathematical Society
Volume	18
Issue number	8
DOIs	https://doi.org/10.4171/JEMS/628
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

Diagonal group
Lattices
Stable

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/628

Cite this

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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.",

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AB - 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.

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KW - Stable

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Stable lattices and the diagonal group

Abstract

Keywords

ASJC Scopus subject areas

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