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

Abstract

Let F be a non-archimedean local field of characteristic zero. Jacquet, Piatetski-Shapiro and Shalika introduced the notion of newforms for irreducible generic representations of GLn(F ). In this paper, we give an explicit formula for Whittaker functions associated to newforms on the diagonal matrices in GLn(F ).

Local Newforms and Formal Exterior Square L-Functions

“…For simplicity, we say that an element W in W(π, ψ) is a newform if W is the Whittaker function associated to a newform for π. It follows from [17] Theorem 4.1 and [18]…”

“…Jacquet, Piatetski-Shapiro and Shalika introduced the concept of newforms for generic representations of GL n (F ) in [10], which is an extension of that of spherical vectors for unramified representations. Recently, Matringe [16] and the first author [17] independently gave an explicit formula for Whittaker functions associated to newforms on the diagonal torus. We apply this formula to compute the integral J(s, W, Φ) when W is associated to a newform.…”