Asai-Flach classes and p-adic L-functions

TL;DR

This paper establishes a formula connecting the Bloch-Kato logarithm of a class in the Asai-Flach Euler system to a p-adic L-function, extending understanding of special values outside the interpolation range.

Contribution

It proves a new explicit formula linking the Bloch-Kato logarithm to the p-adic Asai L-function for quadratic Hilbert modular forms.

Findings

Derived a formula for the Bloch-Kato logarithm of the bottom class.

Expressed the logarithm as a value of the p-adic Asai L-function outside the interpolation range.

Enhanced the understanding of the relationship between Euler systems and p-adic L-functions.

Abstract

We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler system associated to a quadratic Hilbert modular form. We show that this can be expressed as a value, outside the interpolation range, of the p-adic Asai L-function constructed in the prequel paper arXiv:2307.07004.