  Dielectric and magnetic properties have been studied for poly-crystalline
samples of quasi-one-dimensional frustrated spin-1/2 system
Rb$_{2}$(Cu$_{1-x}$M$_{x}$)$_{2}$Mo$_{3}$O$_{12}$(M=Ni and Zn) which does not
exhibit a three-dimensional magnetic transition due to quantum spin fluctuation
and low dimensionality. A broad peak in the magnetic susceptibility -
temperature curves originated from a short range helical ordering at low
temperature is suppressed by the Ni and Zn substitution for Cu sites. The
capacitance is found to anomalously increase with decreasing T below ~50 K,
which is also suppressed by the impurity doping. The behavior of the anomalous
capacitance component is found to be strongly connected with that of the
magnetic susceptibility for Rb$_{2}$(Cu$_{1-x}$M$_{x}$)$_{2}$Mo$_{3}$O$_{12}$
which indicates that the low-temperature dielectric response is driven by the
magnetism.
