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

TL;DR

This paper extends the construction of $p$-adic Asai $L$-functions from imaginary quadratic fields to general CM fields for automorphic representations of ${ m GL}_2$, broadening the scope of $p$-adic $L$-function theory.

Contribution

It generalizes the construction of $p$-adic Asai $L$-functions from imaginary quadratic fields to all CM fields for ${ m GL}_2$ automorphic representations.

Findings

Constructs $p$-adic Asai $L$-functions for general CM fields.

Extends previous work from imaginary quadratic to general CM fields.

Provides a framework for further study of automorphic $L$-functions 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.