A logarithm law for automorphism groups of trees

Sa'ar Hersonsky; Frédéric Paulin

doi:10.1007/s00013-006-1813-8

A logarithm law for automorphism groups of trees

Sa'ar Hersonsky, Frédéric Paulin

Research output: Contribution to journal › Article › peer-review

11 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 sign_q by rational fractions in X over double-struck F sign_q satisfying some congruence properties.

Original language	English
Pages (from-to)	97-108
Number of pages	12
Journal	Archiv der Mathematik
Volume	88
Issue number	2
DOIs	https://doi.org/10.1007/s00013-006-1813-8
State	Published - 1 Jan 2007
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s00013-006-1813-8

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title = "A logarithm law for automorphism groups of trees",

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.",

keywords = "Bruhat-Tits tree, Diophantine equation, Formal Laurent series, Logarithm law, Tree lattice",

author = "Sa'ar Hersonsky and Fr{\'e}d{\'e}ric Paulin",

note = "Funding Information: Acknowledgement. The second author acknowledges the support of the University of Georgia for a stay during which this paper was written.",

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AU - Hersonsky, Sa'ar

AU - Paulin, Frédéric

N1 - Funding Information: Acknowledgement. The second author acknowledges the support of the University of Georgia for a stay during which this paper was written.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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.

AB - 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.

KW - Bruhat-Tits tree

KW - Diophantine equation

KW - Formal Laurent series

KW - Logarithm law

KW - Tree lattice

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DO - 10.1007/s00013-006-1813-8

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SP - 97

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JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 2

ER -

A logarithm law for automorphism groups of trees

Abstract

Keywords

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