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Counting intrinsic Diophantine approximations in simple algebraic groups

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Abstract

We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple algebraic groups, at arbitrarily small scales.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental research, Homi Bhabha Road, Mumbai, 400005, India

    Anish Ghosh

  2. Department of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Alexander Gorodnik

  3. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Amos Nevo

Authors
  1. Anish Ghosh
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  2. Alexander Gorodnik
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  3. Amos Nevo
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Corresponding author

Correspondence to Amos Nevo.

Additional information

To Benjy Weiss, with best wishes for his 80th birthday

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Ghosh, A., Gorodnik, A. & Nevo, A. Counting intrinsic Diophantine approximations in simple algebraic groups. Isr. J. Math. 251, 443–466 (2022). https://doi.org/10.1007/s11856-022-2428-x

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  • DOI: https://doi.org/10.1007/s11856-022-2428-x

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