Relative Trace Formula and Uniform non-vanishing of Central $L$-values of Hilbert Modular Forms

Let $\mathcal{F}(\mathbf{k},\mathfrak{q})$ be the set of normalized Hilbert newforms of weight $\mathbf{k}$ and prime level $\mathfrak{q}$. In this paper, utilizing regularized relative trace formulas, we establish a positive proportion of $\#\{\pi\in\mathcal{F}(\mathbf{k},\mathfrak{q}):L(1/2,\pi)\n...

Full description

Saved in:
Bibliographic Details
Main Authors Wei, Zhining, Yang, Liyang, Zhao, Shifan
Format Journal Article
LanguageEnglish
Published 12.10.2024
Subjects
Mathematics - Number Theory
Online AccessGet full text

Cover

More Information
Summary:Let $\mathcal{F}(\mathbf{k},\mathfrak{q})$ be the set of normalized Hilbert newforms of weight $\mathbf{k}$ and prime level $\mathfrak{q}$. In this paper, utilizing regularized relative trace formulas, we establish a positive proportion of $\#\{\pi\in\mathcal{F}(\mathbf{k},\mathfrak{q}):L(1/2,\pi)\neq 0\}$ as $\#\mathcal{F}(\mathbf{k},\mathfrak{q})\to+\infty$. Moreover, our result matches the strength of the best known results in both the level and weight aspects.
DOI:10.48550/arxiv.2410.09593