Local newforms and formal exterior square l-functions

Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GL_n(F). In this paper, we show that the Jacquet-Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations. Local newform, exterior square L-function, Rankin-Selberg method, zeta integral 22E50, 22E35