On \(p\)-adic L-functions of \(GL(2)\times GL(2)\) over totally real fields (Q2277509)

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.