Whittaker-Shintani functions for general linear groups over p-adic fields

Abstract

In this paper, we recreate the Whittaker-Shintani functions for general linear groups over non-archimedean fields given by Kato et al.Those generalized spherical functions naturally arise from global zeta integrals of automorphic $L$-functions.More explicitly, this formula plays a fundamental role in the local calculation over the split places of tensor product $L$-functions defined by Jiang and Zhang (2014) and the twisted automorphic descents introduced by Jiang and Zhang (2015).