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

In this paper, we recreate the Whittaker-Shintani functions for general linear groups over nonarchimedean 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).