论文标题
高斯领域中二次Hecke $ l $ functions的比率猜想
Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field
论文作者
论文摘要
我们将$ l $ functions的比率猜测为分子和分母在某些范围内使用多个dirichlet系列的Quassian fielders the Quadratic Hecke $ l $ runctions的某些范围中的分母，并在概括性的riemann假设下进行。我们还获得了同一家族$ l $ functions中心值的第一刻的渐近公式，获得了$ o（x^{1/2+\ varepsilon}）$的误差项。
We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of $L$-functions, obtaining an error term of size $O(X^{1/2+\varepsilon})$.
