Values of quadratic forms on quasicrystals and a related problem
Number Theory
2018-02-05 v2 Dynamical Systems
Abstract
In this paper we study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit closure classification type result in this setting. This result has additional applications. In particular, we use it to study the set of integral values of a system consisting of a quadratic form and several linear forms.
Keywords
Cite
@article{arxiv.1711.00411,
title = {Values of quadratic forms on quasicrystals and a related problem},
author = {Oliver Sargent},
journal= {arXiv preprint arXiv:1711.00411},
year = {2018}
}
Comments
18 pages - There is a serious mistake in the proofs of Lemma 2.3 and Theorem 2.1 and also a mistake in the proof of Lemma 4.5. These mistakes have been pointed out to me by Rene Ruhr to whom I am now greatly indebted