P-adic Asai L-functions for quadratic Hilbert eigenforms
Number Theory
2026-01-08 v4
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.
Cite
@article{arxiv.2307.07004,
title = {P-adic Asai L-functions for quadratic Hilbert eigenforms},
author = {Giada Grossi and David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:2307.07004},
year = {2026}
}
Comments
28 pages. Revised (v4) - substantial changes to control and classicity theorems (using geometry of spherical-level Hilbert variety rather than Iwahori-level), added proof of concentration in one degree for cuspidal complex when $k_2 \ne \{0, 1, 2\}$