On the $L^{2}$-restriction norm problem for closed geodesics on the modular surface
| Autor: | Ali, Dana Abou |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $f$ be a Petersson normalized Hecke-Maass cusp form with spectral parameter $t\geq 2$ and let $\mathcal{C}_{D}$ be the union of closed geodesics in $\text{Sl}_{2}(\mathbb{Z})\setminus \mathbb{H}$ associated to a fundamental discriminant $D>0$. Following a suggestion by Sarnak in his letter to Reznikov, we express the restriction norm $||f|_{\mathcal{C}_{D}}||_{2}^{2}$ as a weighted sum of central values of L-functions using Waldspurger's formula. This allows us to get an unconditional improvement over the current bounds. Comment: 18 pages |
| Databáze: | arXiv |
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