The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
Number Theory
2025-03-28 v3
Abstract
We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at least 2. More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of of parallel weight, where is any CM field. We deduce these theorems from a new potential automorphy theorem for the symmetric powers of 2-dimensional compatible systems of Galois representations of parallel weight.
Cite
@article{arxiv.2309.15880,
title = {The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms},
author = {George Boxer and Frank Calegari and Toby Gee and James Newton and Jack A. Thorne},
journal= {arXiv preprint arXiv:2309.15880},
year = {2025}
}
Comments
v2: 74 pages. Minor changes. This is the accepted version. v3: Minor correction in section 2.1