A construction of $p$-adic Asai $L$-functions for ${\rm GL}_2$ over CM fields

Abstract

We give a construction of $p$-adic Asai $L$-functions for cohomological cuspidal automorphic representations of ${\rm GL}_2$ over CM fields. If the base field is imaginary quadratic, Loeffler-Williams recently constructed the $p$-adic Asai $L$-functions. We generalize their construction to the case that the base fields are general CM fields.