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  3. Thin Groups and Superstrong Approximation
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2025
      February 2014
      ISBN:
      9781009701228
      9781107036857
      DOI:
      https://doi.org/10.1017/9781009701228
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.66kg, 376 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Real and Complex Analysis, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Mathematical Sciences Research Institute Publications (61)
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    Subjects:
    Mathematics, Real and Complex Analysis, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Mathematical Sciences Research Institute Publications (61)
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    Book description

    This collection of survey and research articles focuses on recent developments concerning various quantitative aspects of 'thin groups'. There are discrete subgroups of semisimple Lie groups that are both big (i.e. Zariski dense) and small (i.e. of infinite co-volume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading, for instance, to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap, referred to as superstrong approximation. This book provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory and combinatorics. It is suitable for professional mathematicians and graduate students in mathematics interested in this fascinating area of research.

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