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On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

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 G L ( 2 ) × G L ( 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.

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