Eisenstein series on arithmetic quotients of loop groups

We construct Eisenstein series on arithmetic quotients of loop groups, give a convergence criterion, and compute their constant term in terms of the Riemann zeta function. We also give a description of certain measures which will provide in infinite dimensions, the convolution operators needed to obtain an analytic continuation. In the last two sections we discuss the question of volumes of arithmetic quotients, and we discuss various generalizations of our results.

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Published 1 January 1999