Open AccessGeometric estimates for the trace formula
Author(s) -
Werner Hoffmann
Publication year - 2008
Publication title -
annals of global analysis and geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.776
H-Index - 37
eISSN - 1572-9060
pISSN - 0232-704X
DOI - 10.1007/s10455-008-9105-0
Subject(s) - mathematics , trace (psycholinguistics) , quotient , pure mathematics , lattice (music) , rank (graph theory) , geometric mean , combinatorics , geometry , philosophy , linguistics , physics , acoustics
In order to study the asymptotic distribution of geometric or spectral data associated with quotients of a reductive group by a lattice, one needs a trace formula for test functions on that group with noncompact support. Arthur has proved a trace formula for compactly supported test functions on reductive groups of arbitrary rank. We show that the coarse geometric expansion in his formula converges for rapidly decreasing functions. Mathematics Subject Classification. Primary: 11F72; Secondary: 22E55.
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