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

Zhining Wei, Liyang Yang, Shifan Zhao

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 rel…