  This paper considers the downlink of an ultra-reliable low-latency
communication (URLLC) system in which a base station (BS) serves multiple
single-antenna users in the short (finite) blocklength (FBL) regime with the
assistance of a reconfigurable intelligent surface (RIS). In the FBL regime,
the users' achievable rates are complex functions of the beamforming vectors
and of the RIS's programmable reflecting elements (PREs). We propose the joint
design of the transmit beamformers and PREs, the problem of maximizing the
geometric mean (GM) of these rates (GM-rate) and show that this aforementioned
results are providing fair rate distribution and thus reliable links to all
users. A novel computational algorithm is developed, which is based on closed
forms to generate improved feasible points, using its execution. The
simulations show the merit of our solution.
