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The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms. (arXiv:2309.15880v1 [math.NT]) http://arxiv.org/abs/2309.15880

The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms

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.

arxiv.org
September 29, 2023 at 3:10 AM · · feed2toot · 0 · 0 · 0
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