On simultaneous non-vanishing of modular <Emphasis Type="Italic">L</Emphasis>-functions

For i = 1, , r, let f _i be newforms of weight 2k _i for Γ₀(N _i ) with trivial character. We consider the simultaneous non-vanishing problem for the central values of twisted L-functions of f _i . By using the Shimura correspondence, we give a certain relation between this problem and the kernel fields of 2-adic Galois representations associated to modular forms. Received: 28 January 2006