The object of the present note (which is an addendum to [R. Balasubramanian and K. Ramachandra, Indian J. Pure Appl. Math. 18 (1987), no. 9, 790--793]) is to make a few remarks on the results and prove that a certain quasi $L$-function $L(s,\chi)$ is uniformly convergent in any compact subset, and that it can be continued as an entire function.