EISENSTEIN SERIES ON LOOP GROUPS: MAASS-SELBERG RELATIONS 4

摘要

This is the final paper in a series concerning Maass-Selberg relations on arithmetic quotients of loop groups (see [MSI], [MS2], [MS3]).. In [MS3], we established these relations for wave packets of truncated Eisenstein series (see (1.2), below). In the present paper, we do so for truncated Eisenstein series themselves, a result which can be extracted from the relations for wave packets We begin with a posi-tivity result for the function H(/u, p') (see Theorem 1.2 and Corollary 2), which will be fundamental for establishing the remaining results of the paper.