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 $\pi$ of GL_n(F). In this paper, we show that Jacquet-Shalika integral attains a certain L-function, so called the formal exterior square L-function, when the Whittaker function is associated to a newform for $\pi$. By consideration on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations.

12 pages

References in corpus (2)

• Essential Whittaker functions for GL(n)
• Whittaker functions associated to newforms for GL(n) over p-adic fields

Cited by in corpus (5)

• The functional equation of the Jacquet-Shalika integral representation of the local exterior-square $L$-function
• Shalika periods and parabolic induction for GL(n) over a non archimedean local field
• A class number formula for Picard modular surfaces
• The local period integrals and essential vectors
• Derivatives and Exceptional Poles of the Local Exterior Square $L$-Function for $G{L}_m$