 
Summary: ON SOME PROBLEMS SUGGESTED BV THE TRACE FORMULA
Janes Arthur
University of Toronto
Toronto, Ontario, Canada
MS5 1A1
In the present theory of autonorphic representations, a riaior coal
is to stabilize the trace formula. Its realization will have irinortant
conseuuences, among which will be the proof of functorialitv in a
significant number of cases. However, it will recruire much effort, for
there are a number of difficult problems to be solved first. Pone of
the problems, especially those concerning orbital integrals, were
studied in [9(e)l. They arise when one tries to interpret one side of
the trace formula. The other side of the trace formla leads to a
different set of problems. Amon? these, for examle, are questions
relatinq to the nontempered autonorphic representations which occur
discretely. Our purpose here is to describe some of these problems
and to suqqest possible solutions.
Some of the problems have in fact been formulated as conjectures.
They have perhaps been stated in greater detail than is justifieri,
for I have not had sufficient tine to ponder then. However, thev seem
