On the $L^2$ restriction norm of large level

Abstract

In this paper, we prove the mass equidistribution theorem restricted to vertical geodesic segments for holomorphic Hecke newforms of large square-free level. We utilize the effective proof of QUE in the level aspect. Moreover, we study this $L^2$ mass in the full geodesics and relate it to second moments of twisted $L$-functions.

18 pages. Published in IMRN. Comments welcome

References in corpus (7)

• Distribution of mass of holomorphic cusp forms
• The second moment of twisted modular L-functions
• Nodal domains of Maass forms I
• On moments of twisted $L$-functions
• The quantum unique ergodicity conjecture for thin sets
• Equidistribution of cusp forms in the level aspect
• Equidistribution in Shrinking Sets and L^4-Norm Bounds for Automorphic Forms