Convergence of a sum involving the divisor function and characters

Could someone please show me that $\sum_{n = 1}^{\infty} \sigma_{x}(n)n^{-(x + 1)/2} \chi(n)$ converges where $\chi$ is a Dirichlet character of modulus $m$?

• For what $x$ are you interested in? – davidlowryduda Sep 6 '15 at 22:33
• I am interested in -1 < x < 1. – Hugh G Rection Sep 7 '15 at 3:49