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Fuglede’s conjecture holds in \(\mathbb {Q}_{p}\)

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Abstract

We prove Fuglede’s conjecture in \(\mathbb {Q}_p\) which states that a Borel set of positive and finite Haar measure in \(\mathbb {Q}_{p}\) is a spectral set if and only if it tiles \(\mathbb {Q}_p\) by translations.

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Author notes

  1. Ruxi Shi

    Present address: Department of Mathematical sciences, University of Oulu, 90014, Oulu, Finland

Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Aihua Fan & Shilei Fan

  2. LAMFA, UMR 7352 CNRS, Université de Picardie, 33 rue Saint Leu, 80039, Amiens, France

    Aihua Fan & Ruxi Shi

  3. LAMA, UMR 8050, CNRS, Université Paris-Est Créteil, 61 Avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Lingmin Liao

Authors
  1. Aihua Fan
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  2. Shilei Fan
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  3. Lingmin Liao
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Correspondence to Aihua Fan.

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Communicated by A. Venkatesh.

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A. H. FAN was supported by NSF of China (Grant no. 11471132); S. L. FAN was supported by NSF of China (Grant no. 11401236) and Fundamental Research Funds for the Central Universities (Grant no. CCNU19QN076).

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Fan, A., Fan, S., Liao, L. et al. Fuglede’s conjecture holds in \(\mathbb {Q}_{p}\). Math. Ann. 375, 315–341 (2019). https://doi.org/10.1007/s00208-019-01867-8

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  • DOI: https://doi.org/10.1007/s00208-019-01867-8

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