P-adic Asai L-functions for quadratic Hilbert eigenforms

TL;DR

This paper constructs p-adic Asai L-functions for quadratic Hilbert eigenforms using advanced Hida theory on Hilbert modular surfaces, providing new tools for understanding automorphic representations over real quadratic fields.

Contribution

It introduces a novel construction of p-adic Asai L-functions for GL2 over real quadratic fields employing higher Hida theory and Iwahori level structures.

Findings

Successful construction of p-adic Asai L-functions for specified automorphic representations.

Application of higher Hida theory to Hilbert modular surfaces with Iwahori level.

Framework enabling further study of automorphic forms over quadratic fields.

Abstract

We construct p-adic Asai L-functions for cuspidal automorphic representations of GL2 / F, where F is a real quadratic field in which p splits. Our method relies on higher Hida theory for Hilbert modular surfaces with Iwahori level at one prime above p.