Atkin-Lehner Decompositions for Quaternionic modular forms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917075265519616 |
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| author | Cherukara, Siddharth Ramakrishnan |
| author_facet | Cherukara, Siddharth Ramakrishnan |
| contents | In this paper, we obtain Atkin--Lehner decompositions for spaces of modular forms on definite quaternion algebras. Similar to Casselman's approach our methods are representation theoretic. Using Jacquet--Langlands correspondence we also obtain isomorphisms between spaces of quaternionic modular forms and corresponding spaces of Hilbert modular forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atkin-Lehner Decompositions for Quaternionic modular forms Cherukara, Siddharth Ramakrishnan Number Theory Representation Theory In this paper, we obtain Atkin--Lehner decompositions for spaces of modular forms on definite quaternion algebras. Similar to Casselman's approach our methods are representation theoretic. Using Jacquet--Langlands correspondence we also obtain isomorphisms between spaces of quaternionic modular forms and corresponding spaces of Hilbert modular forms. |
| title | Atkin-Lehner Decompositions for Quaternionic modular forms |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2511.06584 |