Abstract
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.
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Hoffmann, W. Geometric estimates for the trace formula. Ann Glob Anal Geom 34, 233–261 (2008). https://doi.org/10.1007/s10455-008-9105-0
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DOI: https://doi.org/10.1007/s10455-008-9105-0