Mass Distribution for holomorphic cusp forms on the vertical geodesic
Number Theory
2024-08-29 v1
Abstract
We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth compactly supported test functions. As an application we show that almost all holomorphic Hecke cusp forms, whose weights are in a short interval, satisfy QUE conjecture on the vertical geodesic.
Keywords
Cite
@article{arxiv.2408.15259,
title = {Mass Distribution for holomorphic cusp forms on the vertical geodesic},
author = {Qingfeng Sun and Qizhi Zhang},
journal= {arXiv preprint arXiv:2408.15259},
year = {2024}
}
Comments
22 pages. arXiv admin note: substantial text overlap with arXiv:2111.04713 by other authors