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

Chengliang Guo

doi:10.1093/imrn/rnag140

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

Number Theory 2026-08-05 v1

Authors: Chengliang Guo

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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.

Keywords

mass equidistribution Hecke newforms large level quantum unique ergodicity geodesic segments L-functions

Cite

@article{arxiv.2608.04597,
  title  = {On the $L^2$ restriction norm of large level},
  author = {Chengliang Guo},
  journal= {arXiv preprint arXiv:2608.04597},
  year   = {2026}
}

Comments

18 pages. Published in IMRN. Comments welcome