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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| Format: | Article |
| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Pi |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508624000295/type/journal_article |
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| author | George Boxer Frank Calegari Toby Gee James Newton Jack A. Thorne |
| author_facet | George Boxer Frank Calegari Toby Gee James Newton Jack A. Thorne |
| author_sort | George Boxer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d66886d708b340feafe0ea1db7b653fc |
| institution | OA Journals |
| issn | 2050-5086 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj-art-d66886d708b340feafe0ea1db7b653fc2025-08-20T02:14:38ZengCambridge University PressForum of Mathematics, Pi2050-50862025-01-011310.1017/fmp.2024.29The Ramanujan and Sato–Tate Conjectures for Bianchi modular formsGeorge Boxer0Frank Calegari1Toby Gee2James Newton3https://orcid.org/0000-0002-9332-5204Jack A. Thorne4https://orcid.org/0000-0002-5900-3260Department of Mathematics, Imperial College London, London SW7 2AZ, UK; E-mail:The University of Chicago, 5734 S University Ave, Chicago, IL 60637, USA; E-mail:Department of Mathematics, Imperial College London, London SW7 2AZ, UK; E-mail:Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK;Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, UK; E-mail: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.https://www.cambridge.org/core/product/identifier/S2050508624000295/type/journal_article11F5511F80 |
| spellingShingle | George Boxer Frank Calegari Toby Gee James Newton Jack A. Thorne The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms Forum of Mathematics, Pi 11F55 11F80 |
| title | The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms |
| title_full | The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms |
| title_fullStr | The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms |
| title_full_unstemmed | The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms |
| title_short | The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms |
| title_sort | ramanujan and sato tate conjectures for bianchi modular forms |
| topic | 11F55 11F80 |
| url | https://www.cambridge.org/core/product/identifier/S2050508624000295/type/journal_article |
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