Abstract
This paper is concerned with the study of diffraction intensities of a relevant class of binary Pisot substitutions via exponential sums. Arithmetic properties of algebraic integers are used to give a new and constructive proof of the fact that there are no diffraction intensities outside the Fourier module of the underlying cut and project schemes. The results are then applied in the context of random substitutions.
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Acknowledgments
The author wishes to thank Michael Baake for helpful discussions and two anonymous referees for useful comments. This work is supported by the German Research Foundation (DFG) via the Collaborative Research Centre (CRC 701) through the faculty of Mathematics, Bielefeld University.
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Communicated by A. Constantin.
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Spindeler, T. Diffraction intensities of a class of binary Pisot substitutions via exponential sums. Monatsh Math 182, 143–153 (2017). https://doi.org/10.1007/s00605-016-0956-3
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DOI: https://doi.org/10.1007/s00605-016-0956-3