Summary: Doc. MATH.J. DMV
ABSTRACT. The paper is a report on the problem of stabilizing the
trace formula. The goal is the construction and analysis of a stable trace
formula that can be used to compare automorphic representations on
1991 Mathematics Subject Classification: Primary 22E55, 11R39.
1. It is an important problem to place the automorphic representation theory
of classical groups on an equal footing with that of GL(n). Thirty years after
the study of GL(2) by Jacquet-Langlands , the theory for GL(n) is now in
pretty good shape. It includes an understanding of the relevant L-functions ,a
classification of the discrete spectrum and cyclic base change [lo]. One would
like to establish similar things for orthogonal, symplectic and unitary groups. A
satisfactory solution would have many applications to number theory, the extent
of which is hard to even guess at present.
A general strategy has been known for some time. One would like to com-
pare trace formulas for classical groups with a twisted trace formula for GL(n).
There is now a trace formula that applies to any group . However, it contains
terms that are complicated, and are hard to compare with similar terms for other
groups. The general comparison problem has first to be formulated more pre-
cisely, as that of stabilizing the trace formula . In this form, the problem is to