LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS

Abstract

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.