 
Summary: ENDOSCOPIC LFUNCTIONS AND A COMBINATORIAL IDENTITY
James Arthur*
1. Introduction. In this paper we shall prove a combinatorial identity for certain
functions attached to reductive algebraic groups over number fields. The functions are
built out of logarithmic derivatives of Lfunctions, and occur as terms on the spectral side
of the trace formula. The identity is suggested by the problem of stabilizing the trace
formula.
We shall say nothing about the general problem, since we will be dealing with only
a small part of it here. For a given group G (which for the introduction we assume is
semisimple and simply connected), together with a Levi subgroup M, we shall define a
function rG
M (c) of a complex variable . The symbol c represents a family {cv : v V }
of semisimple conjugacy classes from the local Lgroups L
Mv. The function rG
M (c) is
constructed in a familiar way from the quotients
rQP (c) = L(0, c, QP )L(1, c, QP )1
, Q, P P(M),
of unramified Lfunctions
L(s, c, QP ) =
