Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2)

Abstract

In this article, we give explicit formulas of archimedean Whittaker functions on G L ( 3 ) GL(3) and G L ( 2 ) GL(2) . Moreover, we apply those to the calculation of archimedean zeta integrals for G L ( 3 ) × G L ( 2 ) GL(3)\times GL(2) , and show that the zeta integral for appropriate Whittaker functions is equal to the associated L L -factors.