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arXiv · 2410.09593

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

Zhining Wei·Liyang Yang·Shifan Zhao
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Abstract

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.

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Zhining Wei, Liyang Yang, Shifan Zhao. 2024-10-12. Relative Trace Formula and Uniform non-vanishing of Central $L$-values of Hilbert Modular Forms. https://arxiv.org/abs/2410.09593

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