$p$-adic Asai $L$-functions attached to Bianchi cusp forms

TL;DR

This paper proves a rationality property for twisted Asai L-values linked to Bianchi cusp forms and constructs distributions that interpolate these values, outlining steps to show they originate from a measure.

Contribution

It introduces a new rationality result for Asai L-values and constructs interpolating distributions, advancing understanding of p-adic L-functions for Bianchi forms.

Findings

Established rationality of twisted Asai L-values.

Constructed distributions interpolating L-values.

Outlined steps to prove these distributions are measures.

Abstract

We establish a rationality result for the twisted Asai L-values attached to a Bianchi cusp form and construct distributions interpolating these L-values. Using the method of abstract Kummer congruences, we then outline the main steps needed to show that these distributions come from a measure.