Abstract
We introduce a 1-cocycle Z of the group G=PGL2(Q) with values in a module D of distributions (in the sense of Stevens and Hu-Solomon). This cocycle is essentially constructed from the Barnes' double zeta function and it has the advantage of defining a family of maps that depend meromorphically on the usual parameter s∈C. In particular, this permits the extension of the cocycle property to any Taylor coefficient of such zeta function at s=0. Furthermore, we show that the class of Z in the first cohomology group H1(G,D) is nonzero, and we use basic facts about the arithmetic of real quadratic fields to prove the vanishing of H0(G,D), the group of G-invariant elements in D.
Published Version
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