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LATTICES OF MINIMAL COVOLUME IN SL2 OVER LOCAL FIELDS

Published online by Cambridge University Press:  01 March 1999

A. LUBOTZKY  and
TH. WEIGEL
A. LUBOTZKY
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel. E-mail:alexlub@math.huji.ac.il
TH. WEIGEL
Affiliation:
Mathematisches Institut, Universität Freiburg, Eckerstrasse 1 D-79104, Freiburg, Germany. Present address: School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London EC1 4NS. E-mail:t.weigel@qmw.ac.uk
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Abstract

Let $K$ be a non-archimedean local field of characteristic $0$ with residue class field not of characteristic $2$. In this note we will determine the minimal covolume $\mu(\mbox{SL}_2(K)/\Gamma)$ of a lattice $\Gamma$ in $\mbox{SL}_2(K)$. Furthermore, we describe all lattices of minimal covolume in terms of their associated graphs of groups and hence up to isomorphism.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 78 , Issue 2 , March 1999 , pp. 283 - 333
Copyright
1999 The London Mathematical Society

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