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

Hida, Haruzo

Ann. Inst. Fourier 41, No. 2, 311-391 (1991).

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.

Reviewer: H.Hida (Los Angeles)

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

Keywords:

interpolation; Rankin product L-function; Hilbert cusp forms; automorphic representation; p-adic analytic function

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