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Lattices of Minimal Covolume in SL 2 Over Local Fields
Author(s) -
Lubotzky A.,
Weigel TH.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599001689
Subject(s) - mathematics , isomorphism (crystallography) , mathematics subject classification , lattice (music) , local field , pure mathematics , field (mathematics) , class (philosophy) , combinatorics , geometry , epistemology , crystallography , physics , crystal structure , chemistry , philosophy , acoustics
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 μSL 2 K /Γ of a lattice Γ in SL 2 K . Furthermore, we describe all lattices of minimal covolume in terms of their associated graphs of groups and hence up to isomorphism. 1991 Mathematics Subject Classification : 20E08, 20G25.