Triple product formula and mass equidistribution on modular curves of level N

Yueke Hu Swiss Federal Institute of Technology in Zürich, Rämistrasse, Zürich, Switzerland

Number Theory mathscidoc:2206.24007

International Mathematics Research Notices, 2018, (9), 2899-2943, 2018.5
Let N be a fixed integer and f be a holomorphic newform of level q⁠, weight k and trivial nebentypus, where q is a multiple of N⁠. In this article, we prove that the pushforward to the modular curve of level N of the mass measure of f tends weakly to the Haar measure as qk→∞⁠. This generalizes the previous results for modular curve of level 1. The main innovation of this article is to obtain an upper bound for the local integral which cancels the convexity bound of the corresponding L-function in level aspect.
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@inproceedings{yueke2018triple,
  title={Triple product formula and mass equidistribution on modular curves of level N},
  author={Yueke Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626173925800280482},
  booktitle={International Mathematics Research Notices},
  volume={2018},
  number={9},
  pages={2899-2943},
  year={2018},
}
Yueke Hu. Triple product formula and mass equidistribution on modular curves of level N. 2018. Vol. 2018. In International Mathematics Research Notices. pp.2899-2943. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626173925800280482.
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