|
This article is available for purchase or by subscription. See below.
Abstract
|
|
We show that there are infinitely many counterexamples to Minkowski’s conjecture in positive
characteristic regarding uniqueness of the upper bound of the multiplicative covering radius,
, by constructing a
sequence of compact
-orbits
where
obtains its conjectured upper bound. In addition, we show that these orbits, as
well as a slightly larger sequence of orbits, must exhibit complete escape of
mass.
|
PDF Access Denied
We have not been able to recognize your IP address
35.173.48.18
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
compact orbit, diagonal group, function fields, positive
characteristic, Minkowski conjecture, geometry of numbers,
covering radius, measures, escape of mass
|
Mathematical Subject Classification
Primary: 11H46
Secondary: 37A44
|
Milestones
Received: 4 March 2023
Revised: 27 February 2024
Accepted: 30 April 2024
Published: 16 August 2024
|
| © 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
|
