Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Tadashi Miyazaki

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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 $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 1 (2018), 1-6.

First available in Project Euclid: 5 January 2018

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Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 11F30: Fourier coefficients of automorphic forms 22E46: Semisimple Lie groups and their representations

Whittaker functions automorphic forms zeta integrals


Miyazaki, Tadashi. The local zeta integrals for $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 1, 1--6. doi:10.3792/pjaa.94.1.

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