Low-lying zeros of Hilbert modular $L$-functions weighted by powers of central $L$-values

Zhining Wei, Liyang Yang, Shifan Zhao

Let $\mathcal{F}(\text{k},\mathfrak{q})$ be the set of primitive Hilbert modular forms of weight $\text{k}$ and prime level $\mathfrak{q}$, with trivial central character. We s…