The Ramanujan-Petersson and Selberg conjectures for Maass forms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915792955637760 |
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| author | Unterberger, Andr'e |
| author_facet | Unterberger, Andr'e |
| contents | We prove the Ramanujan-Petersson conjecture for Maass forms of the group $SL(2,Z)$, with the help of automorphic distribution theory and pseudodifferential analysis. The first notion is an alternative to classical automorphic function theory, in which the plane takes the place usually ascribed to the hyperbolic half-plane. The Selberg conjecture for Hecke's group $Γ_0(M)$ follows as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_10956 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Ramanujan-Petersson and Selberg conjectures for Maass forms Unterberger, Andr'e Group Theory Number Theory 11F37 35S99 We prove the Ramanujan-Petersson conjecture for Maass forms of the group $SL(2,Z)$, with the help of automorphic distribution theory and pseudodifferential analysis. The first notion is an alternative to classical automorphic function theory, in which the plane takes the place usually ascribed to the hyperbolic half-plane. The Selberg conjecture for Hecke's group $Γ_0(M)$ follows as well. |
| title | The Ramanujan-Petersson and Selberg conjectures for Maass forms |
| topic | Group Theory Number Theory 11F37 35S99 |
| url | https://arxiv.org/abs/2001.10956 |