## A sum of Ramanujan sums

I have the following question about Ramanujan sums. (All vectors and matrices here will be understood to have integer entries.) Let Xq={(x1,…,xR)|1≤xi≤q} and let, for any R×R matrix B with rows bi, cq(Bx):=cq(b1⋅x)…cq(br⋅x), where cq(n) is Ramanujan’s sum. Suppose an R×R matrix A with determinant D is given and denote by I the identity matrix. … Read more