Restricted successive minima

Martin Henk and Carsten Thiel

Vol. 269 (2014), No. 2, 341–354

DOI: 10.2140/pjm.2014.269.341

Abstract

We give bounds on the successive minima of an $o$-symmetric convex body under the restriction that the lattice points realizing the successive minima are not contained in a collection of forbidden sublattices. Our investigations extend former results to forbidden full-dimensional lattices, to all successive minima and complement former results in the lower-dimensional case.

Keywords

successive minima, lattice, convex body, short lattice vectors, forbidden sublattices

Mathematical Subject Classification 2010

Primary: 11H06

Secondary: 52C07

Milestones

Received: 19 February 2013

Revised: 17 May 2013

Accepted: 19 June 2013

Published: 26 July 2014