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Values of quadratic forms on quasicrystals and a related problem

2017/11/01 by Oliver Sargent, Sargent, Oliver
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1711.00411

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

arxiv created 2018/02/02 · arxiv updated 2018/02/05

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.

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