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Vol. 45. No. 4 DUKE MATHEMATICAL JOURNAL@ December 1978 A TRACE FORMULA FOR REDUCTIVE GROUPS I
 

Summary: Vol. 45. No. 4 DUKE MATHEMATICAL JOURNAL@ December 1978
A TRACE FORMULA FOR REDUCTIVE GROUPS I
TERMS ASSOCIATED TO CLASSES IN G(Q)
JAMES G. ARTHUR
Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915
The kernel Kp(x,y) . . . . . . . . . . . . . . . . . . . . . . . . . . 919
A review of Eisenstein series . . . . . . . . . . . . . . . . . . . . . 924
The second formula for the kernel . . . . . . . . . . . . . . . . . . 928
The modified kernel identity . . . . . . . . . . . . . . . . . . . . . 935
Some geometric lemmas . . . . . . . . . . . . . . . . . . . . . . . 938
. . . . . . . . . . . . . . . . . . . . . . . .Integrability of KE(x,f ) 942
Weighted orbital integrals . . . . . . . . . . . . . . . . . . . . . . 947
Introduction
This paper, along with a subsequent one, is an attempt to generalize the
Selberg trace formula to an arbitrary reductive group G defined over the ratio-
nal numbers. Our main results have been announced in the lectures [l(c)].
In his original papers [8(a), (b)], Selberggave a novel formula for the trace of
a certain operator associated with a compact quotient of a semisimple Lie
group and a discrete subgroup. When the discrete subgroup is arithmetic, the
situation is essentially equivalent to the case that the group G is anisotropic.

  

Source: Arthur, James G. - Department of Mathematics, University of Toronto

 

Collections: Mathematics