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Recently Atobe-Oi-Yasuda established the newform theory for irreducibletempered generic representations of unramified ${\rm U}_{2n+1}$ overnon-archimedean local fields. In this paper we extend their result to everyirreducible generic representations and compute the dimensions of the spaces ofoldforms. We also compute the Rankin-Selberg integrals attached to newforms andoldforms under a natural assumption on the $\gamma$-factors defined by theseintegrals.

Local newforms for generic representations of unramified ${\rm U}_{2n+1}$ and Rankin-Selberg integrals