论文标题
随机乘法功能：Selberg-Delange类
Random multiplicative functions: The Selberg-Delange class
论文作者
论文摘要
令$ 1/2 \leqβ<1 $，$ p $为通用质数，$f_β$是在无方形整数上支持的随机乘法函数，使得$（f_β（p））_ {p} $是I.I.D.带有分布的随机变量的顺序$ \ mathbb {p}（f（p）= - 1）=β= 1- \ mathbb {p}（f（p）=+1）$。令$f_β$为$f_β$的dirichlet系列。我们证明了一个公式，涉及衡量标准的转换，将riemann $ζ$与$f_β$的dirichlet系列相关联，用于$β$的某些值，并提供应用程序。此外，我们证明了Riemann假设与$f_β$的一定加权部分总和的平均行为有关。
Let $1/2\leqβ<1$, $p$ be a generic prime number and $f_β$ be a random multiplicative function supported on the squarefree integers such that $(f_β(p))_{p}$ is an i.i.d. sequence of random variables with distribution $\mathbb{P}(f(p)=-1)=β=1-\mathbb{P}(f(p)=+1)$. Let $F_β$ be the Dirichlet series of $f_β$. We prove a formula involving measure-preserving transformations that relates the Riemann $ζ$ function with the Dirichlet series of $F_β$, for certain values of $β$, and give an application. Further, we prove that the Riemann hypothesis is connected with the mean behavior of a certain weighted partial sums of $f_β$.
