Sums of reciprocals of fractional parts

Reynold Fregoli

Let $\mathbf{\alpha }\in {\mathbb{R}}^N$ and $Q\ge 1$. We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbolα\cdot\boldsymbol{q…