This paper investigates two performance metrics, namely ergodic capacity and symbol error rate, of mmWave communication system assisted by a reconfigurable intelligent surface (RIS). We assume independent and identically distributed (i.i.d.) Rician fadings between user-RIS-Access Point (AP), with RIS surface consisting of passive reflecting elements. First, we derive a new unified closed-form formula for the average symbol error probability of generalised M-QAM/M-PSK signalling over this mmWave link. We then obtain new closed-form expressions for the ergodic capacity with and without channel state information (CSI) at the AP.