"In this article, we give explicit formulas of archimedean Whittaker functions on GL(3) and GL(2). Moreover, we apply those to the calculation of archimedean zeta integrals for GL(3) x GL(2), and show that the zeta integral for appropriate Whittaker functions is equal to the associated L-factors"--
In the first part of the book, Hirano, Ishii, and Miyazaki give explicit formulae of Archimedean Whittaker functions for the irreducible (generalized) principal series representations on GL (3) and GL(2). These formulae are essentially the same as in previous papers, they say, but in a refined form applicable to the second part of the book. In that part, they discuss the Archimedean zeta integrals for GL(3) and GL(2) by using their explicit formulae of Whittaker functions. Their explicit evaluation of the Archimedean zeta integrals leads the main results of the study. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
