## 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

### Keywords:

Whittaker functions; automorphic forms; zeta integrals
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### References:

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