The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912296782004224 |
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| author | Boxer, George Calegari, Frank Gee, Toby Newton, James Thorne, Jack A. |
| author_facet | Boxer, George Calegari, Frank Gee, Toby Newton, James Thorne, Jack A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15880 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms Boxer, George Calegari, Frank Gee, Toby Newton, James Thorne, Jack A. Number Theory 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. |
| title | The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2309.15880 |