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| Format: | Preprint |
| Publié: |
2020
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| Accès en ligne: | https://arxiv.org/abs/2004.00284 |
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| _version_ | 1866911532954157056 |
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| author | Unterberger, Andre |
| author_facet | Unterberger, Andre |
| contents | The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an achievement of algebraic geometry. We give here a short analytic proof of the Ramanujan-Deligne theorem, and we shall indicate at the end the close analogy of the proof with that of the Ramanujan-Petersson conjecture for Maass forms [8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_00284 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A unified scheme of approach to the Ramanujan conjecture Unterberger, Andre Number Theory 11F11 The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an achievement of algebraic geometry. We give here a short analytic proof of the Ramanujan-Deligne theorem, and we shall indicate at the end the close analogy of the proof with that of the Ramanujan-Petersson conjecture for Maass forms [8]. |
| title | A unified scheme of approach to the Ramanujan conjecture |
| topic | Number Theory 11F11 |
| url | https://arxiv.org/abs/2004.00284 |