 
Summary: ON A FAMILY OF DISTRIBUTIONS OBTAINED
FROM EISENSTEIN SERIES H: EXPLICIT FORMULAS
Introduction. The purpose of this paper is to find explicit formulas
for those terms in the trace formula which arise from Eisenstein series.
The paper is a continuation of [l(g)]. (We refer the reader to the introduc
tion of [l(g)] for a general discussion as well as a description of the nota
tion we will use below.) We have already solved the most troublesome
analytic problem. The difficulties which remain are largely combinatorial.
Our principal results are Theorems 4.1, 8.1 and 8.2. Theorem 4.1
contains an explicit formula for a polynomial
which was introduced in [l(g)]. (This polynomial depends not only on a
test function B ? C:(i@*/iaÂ¤) but also on a fixed K finite function
f ? C ~ G ( A ) ' )and a fixed class \ ? X.) We will prove Theorem 4.1, not
without some effort, from an asymptotic formula for PT(B)from the pre
vious paper ([l(g), Theorem 7.11). We will then be able to calculate J;(f)
by substituting into the formula
J^f ) = lim P~(B')
â,¬
of [l(g),Theorem 6.31. This will lead directly to Theorem 5.2, which is the
resulting formula for
