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On $$p$$-adic L-functions of $$GL(2)\times GL(2)$$ over totally real fields. (English) Zbl 0725.11025
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(2)$$\times GL(2)$$ 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.

##### MSC:
 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F85 $$p$$-adic theory, local fields 11F33 Congruences for modular and $$p$$-adic modular forms 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
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