}   \frac{\alpha_{{\mathfrak p},0}^k + \cdots + \alpha_{{\mathfrak p},d}^k}{k{{\rm N}}{\mathfrak p}^{ks}} = \sum_{{{\rm N}}({\mathfrak p}) \leq x} \sum_{k \geq 0}  \frac{\alpha_{{\mathfrak p},0}^k + \cdots + \alpha_{{\mathfrak p},d}^k}{k{{\rm N}}{\mathfrak p}^{ks}}  