The local zeta integrals for \(\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})\). (English) Zbl 1446.11098
Summary: In this article, for irreducible admissible infinite-dimensional representations \(\Pi\) and \(\Pi'\) of \(\mathrm{GL}(2,\mathbb{C})\), we show that the local \(L\)-factor \(L(s,\Pi \times \Pi')\) can be expressed as some local zeta integral for \(\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})\).
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 11F30 | Fourier coefficients of automorphic forms |
| 22E46 | Semisimple Lie groups and their representations |
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