The Ramanujan and Sato-Tate conjectures for Bianchi modular forms
File(s)
Author(s)
Boxer, George
Calegari, Frank
Gee, Toby
Newton, James
Thorne, Jack A
Type
Journal Article
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 GL2 (A𝐹 ) of parallel weight, where F 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.
we prove these conjectures for all regular algebraic cuspidal automorphic representations of GL2 (A𝐹 ) of parallel weight, where F 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.
Date Issued
2025-02-21
Date Acceptance
2024-10-27
Citation
Forum of Mathematics, Pi, 2025, 13
ISSN
2050-5086
Publisher
Cambridge University Press
Journal / Book Title
Forum of Mathematics, Pi
Volume
13
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press
License URL
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Subjects
ADIC GALOIS REPRESENTATIONS
AUTOMORPHY
CLASSIFICATION
COHOMOLOGY
MASS EQUIDISTRIBUTION
Mathematics
Mathematics, Applied
Physical Sciences
Science & Technology
VARIETIES
Publication Status
Published
Article Number
e10
Date Publish Online
2025-02-21