### On $p$-adic $L$-functions of $GL\left(2\right)\times GL\left(2\right)$ over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

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Let $D(s,f,g)$ be the Rankin product $L$-function for two Hilbert cusp forms $f$ and $g$. This $L$-function is in fact the standard $L$-function of an automorphic representation of the algebraic group $GL\left(2\right)\times GL\left(2\right)$ defined over a totally real field. Under the ordinarity assumption at a given prime $p$ for $f$ and $g$, we shall construct a $p$-adic analytic function of several variables which interpolates the algebraic part of $D(m,f,g)$ for critical integers $m$, regarding all the ingredients $m$, $f$ and $g$ as variables.