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arXiv · 2309.15880

The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms

George Boxer·Frank Calegari·Toby Gee·James Newton·Jack A. Thorne
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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 $\mathrm{GL}_2(\mathbf{A}_F)$ 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.

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George Boxer, Frank Calegari, Toby Gee, James Newton, Jack A. Thorne. 2023-09-27. The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms. https://arxiv.org/abs/2309.15880

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