让$\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="∕">∕</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="\beta ">\beta </trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="1">1</trans>}$,对是一个通用质数，并且${\mathrm{<trans\; data-src="f">（f）</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}$是支持无平方整数的随机乘法函数，以便${<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="f">（f）</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}_{\mathrm{<trans\; data-src="p">对</trans>}}$是具有分布的随机变量的i.i.d.序列$\mathbb{<trans\; data-src="P">P（P）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="f">（f）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathit{<trans\; data-src="\beta ">\beta </trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="-">-</trans>\mathbb{<trans\; data-src="P">P（P）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="f">（f）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>$.让${\mathrm{<trans\; data-src="F">F类</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}$是Dirichlet级数${\mathrm{<trans\; data-src="f">（f）</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}$.我们证明了一个涉及保测度变换的公式，它与黎曼变换有关ζDirichlet级数函数${\mathrm{<trans\; data-src="F">F类</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}$，对于的某些值β，并给出应用程序。进一步，我们证明了黎曼假设与某个加权部分和的平均行为有关${\mathrm{<trans\; data-src="f">（f）</trans>}}_{\mathit{<trans\; data-src="\beta ">\beta </trans>}}$.