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Mass equidistribution for Saito-Kurokawa lifts

Number Theory 2024-07-04 v3 Analysis of PDEs

Abstract

Let FF be a holomorphic cuspidal Hecke eigenform for Sp4(Z)\mathrm{Sp}_4(\mathbb{Z}) of weight kk that is a Saito--Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of FF equidistributes on the Siegel modular variety as kk\longrightarrow \infty. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity.

Keywords

Cite

@article{arxiv.2309.13009,
  title  = {Mass equidistribution for Saito-Kurokawa lifts},
  author = {Jesse Jääsaari and Stephen Lester and Abhishek Saha},
  journal= {arXiv preprint arXiv:2309.13009},
  year   = {2024}
}

Comments

Accepted version, to appear in GAFA; 58 pages