 
Summary: Vol. 49, No. 1 DUKE MATHEMATICAL JOURNAL 0 March 1982
ON THE INNER PRODUCT OF TRUNCATED
EISENSTEIN SERIES
JAMES ARTHUR
CONTENTS
Introduction . . . . . . . . .
$ 1. The problem . . . . . . . . .
$2. Residues of cuspidal Eisenstein series
83. Exponents . . . . . . . . .
$4. A comparison between two groups .
$5. A property of the truncation operator
$6. The constant terms of Eisenstein series
$7. The negative dual chamber . . . .
$8. Coefficients of the zero exponents . .
$9. Conclusion . . . . . . . . .
Bibliography . . . . . . . . .
Introduction. One can think of Eisenstein series as the spectral kernels for the
LaplaceBeltrami operator on a certain class of noncompact Riemannian
manifolds. They are the eigenfunctions corresponding to the continuous
spectrum. In particular they are not square integrable. However, there is a
