p-adic Asai L-functions of Bianchi modular forms

The Asai (or twisted tensor) L-function of a Bianchi modular form Psi is the L-function attached to the tensor induction to Q of its associated Galois representation. When Psi is ordinary at p we construct a p-adic analogue of this L -function: that is, a p-adic measure on Z(p)(x) that interpolates the critical values of the Asai L-function twisted by Dirichlet characters of p-power conductor. The construction uses techniques analogous to those used by Lei, Zerbes and the first author in order to construct an Euler system attached to the Asai representation of a quadratic Hilbert modular form.