Local newforms for the general linear groups over a non-archimedean local field

Abstract In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups p -adic general linear groups indexed by nonnegative integers and established the theory local newforms for irreducible generic representations. this paper, we extend their results to all To do this, define new certain tuples integers. For proof, introduce Rankin–Selberg integrals Speh