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 $\operatorname {\mathrm {GL}}_2(\mathbf {A}_F)$ of parallel weight, where F is...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508624000295/type/journal_article |
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| Summary: | 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
$\operatorname {\mathrm {GL}}_2(\mathbf {A}_F)$
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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| ISSN: | 2050-5086 |