Abstract

Following a theorem of Hayes, we give a geometric interpretation of the special value at s = 0 of certain 1-cocycle on PGL2(Q) previously introduced by the author. This work yields three main results: an explicit formula for our cocycle at s = 0, a generalization and a new proof of Hayes’ theorem, and an elegant summation formula for the zeroth coefficient of the Ehrhart quasi-polynomial of certain triangles in R2