Archimedean zeta integrals for $GL(3)\times GL(2)$

TL;DR

This paper derives explicit formulas for archimedean Whittaker functions on GL(3) and GL(2), and uses them to compute zeta integrals, confirming their equality to the corresponding L-factors.

Contribution

It provides explicit formulas for archimedean Whittaker functions and applies them to evaluate zeta integrals for GL(3)×GL(2), establishing their connection to L-factors.

Findings

Explicit formulas for archimedean Whittaker functions on GL(3) and GL(2)

Calculation of archimedean zeta integrals for GL(3)×GL(2)

Zeta integrals equal to the associated L-factors for suitable Whittaker functions

Abstract

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 $GL(3)\times GL(2)$, and show that the zeta integral for appropriate Whittaker functions is equal to the associated $L$-factors.