论文标题
在$ l^{2} $ - 模块化表面上关闭的大地测量学的限制规范问题
On the $L^{2}$-restriction norm problem for closed geodesics on the modular surface
论文作者
论文摘要
令$ f $作为彼得克·马斯（Hecke-Maass）的标准化，具有光谱参数$ t \ geq 2 $，让$ \ Mathcal {c} _ {d} $是$ \ text {sl} {sl} _ {2}（2}}（\ nathbb {z} $ a a immines \ natembb {h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h hh hh h h h h h h h h h h h h hh hh hh sl text {sl} _ {sl}判别$ d> 0 $。在Sarnak在给Reznikov的信中提出了建议，我们表达了限制规范$ || f | _ {\ Mathcal {\ Mathcal {C} _ {d}} || _ {2}^{2}^{2} $作为使用Waldspurger的L-LACTIONS的中心值的加权总和。这使我们能够对当前界限进行无条件的改进。
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.
