Jordan Form of (i+j over j) over Z[subscript p]

Abstract

The Jordan Form over field Z[subscript p] of J[superscript p][subscript p]n is diagonal for p > 3 with characteristic polynomial, ϕ(x) = x[superscript 3] - 1, for p prime, n natural number. These matrices have dimension p[superscript n] x p[superscript n], with entries (i+j over j). I prove these results with the method of generating functions.