The mixing conjecture under GRH
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917096655421440 |
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| author | Blomer, Valentin Brumley, Farrell Khayutin, Ilya |
| author_facet | Blomer, Valentin Brumley, Farrell Khayutin, Ilya |
| contents | We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in rational quaternion algebras. The proof is conditional on the Generalized Riemann Hypothesis, and when the division algebra is indefinite we furthermore assume the Ramanujan conjecture. Our methods, which provide an effective rate, are based on the spectral theory of automorphic forms and their $L$-functions, as well as techniques in classical analytic number theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06280 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The mixing conjecture under GRH Blomer, Valentin Brumley, Farrell Khayutin, Ilya Number Theory 11F67, 11N75, 37A44, 37A46, 37A25 We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in rational quaternion algebras. The proof is conditional on the Generalized Riemann Hypothesis, and when the division algebra is indefinite we furthermore assume the Ramanujan conjecture. Our methods, which provide an effective rate, are based on the spectral theory of automorphic forms and their $L$-functions, as well as techniques in classical analytic number theory. |
| title | The mixing conjecture under GRH |
| topic | Number Theory 11F67, 11N75, 37A44, 37A46, 37A25 |
| url | https://arxiv.org/abs/2212.06280 |