论文标题
临界条中希尔伯特模块化形式的L功能的衍生物的无散制
Non-Vanishing of Derivatives of L-Functions of Hilbert Modular Forms in The Critical Strip
论文作者
论文摘要
在本文中，我们表明，平均而言，Cuspidal Hilbert模块化表格的$ L $ runctions的衍生物具有足够大的重量$ k $在行段上不会消失$ \ im \ im（s）= t_ {0} $， $ \ re（s）\ in（\ frac {k-1} {2}，\ frac {k} {2}-ε）\ cup（\ frac {k} {2} {2}+ε，\ frac {k+1} {2} {2} {2} {2}）$。这类似于经典模块化形式的情况。
In this paper, we show that, on average, the derivatives of $L$-functions of cuspidal Hilbert modular forms with sufficiently large weight $k$ do not vanish on the line segments $\Im(s)=t_{0}$, $\Re(s)\in(\frac{k-1}{2},\frac{k}{2}-ε)\cup(\frac{k}{2}+ε,\frac{k+1}{2})$. This is analogous to the case of classical modular forms.
