  Following the work of Harris and Kudla we prove a more general form of a
conjecture of Jacquet relating the non-vanishing of a certain period integral
to non-vanishing of the central critical value of a certain $L$-function. As a
consequence we deduce certain local results about the existence of
$GL_2(k)$-invariant linear forms on irreducible, admissible representations of
$GL_2({\Bbb K})$ for ${\Bbb K}$ a commutative semi-simple cubic algebra over a
non-archimedean local field $k$ in terms of certain local epsilon factors which
were proved only in certain cases by the first author in his earlier work. This
has been achieved by globalising a locally distinguished representation to a
globally distinguished representation, a result of independent interest.
