Shintani cocycles and generalized Dedekind sums

In this thesis, we study Shintani cocycles for PGL$\sb{n}(\doubq)$ and explore their application to generalized Dedekind sums. We give a construction of Shintani cocycles in terms of Shintani generating functions and show that our construction satisfies the cocycle condition in dimensions 1, 2 and 3. The cocycle in dimension 2 gives reciprocity laws for generalized Dedekind sums. In addition, a partial cocycle law in all dimensions (applying to the so-called geometrically non-degenerate cases) gives new linear relations among multiple Dedekind sums