The Shintani Cocycle, : II. Partialζ-Functions, Cohomologous Cocycles andp-adic Interpolation Original Research Article

The “Shintani Cocyle”Φimageis further investigated under three headings. Firstly, a precise link with partialζ-values is given and non-triviality results are deduced for cocycles specializingΦimage. Secondly, a cohomologous “deformation”Ψ∞ofΦ∞(related to cocycles of Scezch and Stevens) is studied by means of explicit formulae. Thirdly, another deformationUpsilon(ν)∞is considered from ap-adic viewpoint and shown to be interpolable. Applications are given to the construction ofp-adic partialζ-functions.