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 \(\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})\).


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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