Superconformal indices on $S^1\times (S^5\mathrm{/}{Z}_p)$

We obtain generating functions associated to the abelian superconformal indices for 6d $(1,0)$ tensor and hypermultiplets on $S^1\times (S^5\mathrm{/}{Z}_p)$. We extract the superconformal indices and their high and low temperature behaviors. We consider round and generically squashed $S^5$ in turn. We show that the unsquashed limit of the superconformal indices is smooth. We examine S-duality in the large $p$ limit that acts by exchanging the Hopf circle with the temporal circle.