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In this paper we show how one can combine the p-adic Rankin-Selberg productconstruction of Hida with freeness results of Hecke modules of Wiles toestablish interesting congruences between special values of L-functions. Thesecongruences is a part of some deep conjectural congruences that follow from thework of Kato on the non-commutative Iwasawa theory of the false Tate curveextension.

Special values of L-functions and false Tate curve extensions II