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Quantitative disjointness of nilflows from horospherical flows

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Abstract

We prove a quantitative variant of a disjointness theorem of nilflows from horospherical flows following a technique of Venkatesh, combined with the structural theorems for nilflows by Green, Tao and Ziegler.

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Acknowledgments

The research was conducted as part of the author’s PhD thesis in the Hebrew University of Jerusalem, under the guidance of Prof. Elon Lindenstrauss. The author also wishes to thank Prof. Tamar Ziegler for helpful conversations regarding nilcharacthers and explaining the inverse theorem of Green-Tao-Ziegler to him. Part of this work was done while the author was visiting MSRI during the program “Analytic Number Theory”. The author wishes to thank MSRI and the organizers for providing excellent working conditions. The research was supported by ERC grant (AdG Grant 267259) and the ISF (grant 891/15).

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Asaf Katz

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48019, USA

    Asaf Katz

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  1. Asaf Katz
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Correspondence to Asaf Katz.

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Katz, A. Quantitative disjointness of nilflows from horospherical flows. JAMA 150, 1–35 (2023). https://doi.org/10.1007/s11854-023-0269-0

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  • DOI: https://doi.org/10.1007/s11854-023-0269-0

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