The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms

2023/09/27 by George Boxer, Frank Calegari, Boxer, George +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2309.15880

openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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(A_F) 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.

Cited by

• Bianchi Modular Forms and the Rationality of Periods

Related

• The Sato-Tate conjecture for Hilbert modular forms
• The Sato-Tate conjecture for modular forms of weight 3
• Potential automorphy over CM fields
• Sharp bounds for multiplicities of Bianchi modular forms
• Genuine Bianchi modular forms of higher level, at varying weight and discriminant