This article is available for purchase or by subscription. See below.
Abstract
|
In order to analyse the simultaneous approximation properties of
reals, the
parametric geometry of numbers studies the joint behaviour of the successive minima
functions with respect to a one-parameter family of convex bodies and a lattice defined in
terms of the
given reals. For simultaneous approximation in the sense of Dirichlet, the linear independence
over
of these reals together with 1 is equivalent to a certain nice intersection property that
any two consecutive minima functions enjoy. This paper focusses on a slightly
generalized version of simultaneous approximation where this equivalence is no longer
in place and investigates conditions for that intersection property in the case of
linearly dependent irrationals.
|
PDF Access Denied
We have not been able to recognize your IP address
34.229.63.28
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
parametric geometry of numbers, successive minima,
simultaneous approximation
|
Mathematical Subject Classification 2010
Primary: 11H06, 11J13
|
Milestones
Received: 17 October 2018
Revised: 20 March 2019
Accepted: 22 May 2019
Published: 23 July 2019
|
|