I am trying to prove that the series $\sum \dfrac {1} {\left( m_{1}^{2}+m_{2}^{2}+\cdots +m_{r }^{2}\right)^{\mu} } $ in which the summation extends over all positive and negative integral values and zero values of $m_1, m_2,\dots, m_r$, except the set of simultaneous zero values, is absolutely convergent if $\mu > \dfrac {r} {2}$.
Any help with a proof strategy would be much appreciated.