A logarithm law for automorphism groups of trees

Sa'ar Hersonsky, Frédéric Paulin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let Γ be a geometrically finite tree lattice. We prove a Khintchine-Sullivan type theorem for the Hausdorff measure of the set of points at infinity of the tree that are well approximated by the parabolic fixed points of Γ. Using Bruhat-Tits trees, an application is given for the Diophantine approximation of formal Laurent series in the variable X -1 over the finite field double-struck F signq by rational fractions in X over double-struck F signq satisfying some congruence properties.

Original languageEnglish
Pages (from-to)97-108
Number of pages12
JournalArchiv der Mathematik
Volume88
Issue number2
DOIs
StatePublished - 1 Jan 2007
Externally publishedYes

Keywords

  • Bruhat-Tits tree
  • Diophantine equation
  • Formal Laurent series
  • Logarithm law
  • Tree lattice

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