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Let F be a non-archimedean local field of characteristic zero. Jacquet andShalika attached a family of zeta integrals to unitary irreducible genericrepresentations $\pi$ of GL_n(F). In this paper, we show that Jacquet-Shalikaintegral attains a certain L-function, so called the formal exterior squareL-function, when the Whittaker function is associated to a newform for $\pi$.By consideration on the Galois side, formal exterior square L-functions areequal to exterior square L-functions for some principal series representations.

Local newforms and formal exterior square L-functions