论文标题
高斯领域的二次hecke $ l $ functions的矩和不变的中心价值
Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field
论文作者
论文摘要
我们评估了高斯领域中Qudratic Hecke $ l $ functions的中心价值的前三个时刻，并使用节省误差项。特别是，我们获得了前两个矩的渐近公式，其尺寸$ o（x^{1/2+\ varepsilon}）$。我们还研究了同一家族的$ l $ functions的第一和第二个动荡的时刻，以表明该家族成员中至少$ 87.5 \％$具有不断变化的中心价值。
We evaluate the first three moments of central values of a family of qudratic Hecke $L$-functions in the Gaussian field with power saving error terms. In particular, we obtain asymptotic formulas for the first two moments with error terms of size $O(X^{1/2+\varepsilon})$. We also study the first and second mollified moments of the same family of $L$-functions to show that at least $87.5\%$ of the members of this family have non-vanishing central values.
