By a Riemann function we mean $f:\mathbb{Z}^n\to\mathbb{Z}$ such that $f(\mathbf{d})$ is equals $0$ for $d_1+\cdots+d_n$ sufficiently small, and $d_1+\cdots+d_n+C$ constant, $C$, large. adding $1$ to the Baker-Norine rank of graph, one gets an equivalent function, similarly related functions.
 To each associate $W: \mathbb{Z}^n\to \mathbb{Z}$ via Möbius inversion call weight function. We g...

Article history: Received 19 May 2011 Available online xxxx