  In this paper we determine the delivery time for a multi-server coded caching
problem when the cache size of each user is small. We propose an achievable
scheme based on coded cache content placement, and employ zero-forcing
techniques at the content delivery phase. Surprisingly, in contrast to previous
multi-server results which were proved to be order-optimal within a
multiplicative factor of 2, for the low memory regime we prove that our
achievable scheme is optimal. Moreover, we compare the performance of our
scheme with the uncoded solution, and show our proposal improvement over the
uncoded scheme. Our results also apply to Degrees-of-Freedom (DoF) analysis of
Multiple-Input Single-Output Broadcast Channels (MISO-BC) with cache-enabled
users, where the multiple-antenna transmitter replaces the role of multiple
servers. This shows that interference management in the low memory regime needs
different caching techniques compared with medium-high memory regimes discussed
in previous works.
