The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the ‘restriction to the rationals’ of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form.

In this talk, I will discuss joint work with David Loeffler in which we construct a p-adic Asai L-function — that is, a distribution on Z_p* that interpolates the critical values L^As(f,chi,1) — for ordinary weight 2 Bianchi modular forms. The method makes use of techniques from the theory of Euler systems, namely Kato’s system of Siegel units, building on the rationality results of Ghate.