The local zeta integrals for $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$

Abstract

In this article, for irreducible admissible infinite-dimensional representations $\Pi$ and $\Pi'$ of $\mathit{GL}(2,\mathbf{C})$, we show that the local $L$-factor $L(s,\Pi \times \Pi')$ can be expressed as some local zeta integral for $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$.