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

In this paper we show how one can combine the p-adic Rankin-Selberg product construction of Hida with freeness results of Hecke modules of Wiles to establish interesting congruences between special values of L-functions. These congruences is a part of some deep conjectural congruences that follow from the work of Kato on the non-commutative Iwasawa theory of the false Tate curve extension.