论文标题
单数系列平均值和Riemann Zeta功能的零
A singular series average and the zeros of the Riemann zeta-function
论文作者
论文摘要
我们表明，Goldbach和Hardy-Littlewood Prime Pair Prime Pair猜想中的单数系列的Riesz平均值具有渐近公式，其误差项可以表示为明确的公式，取决于Riemann Zeta功能的零。无条件地显示，可以证明此误差项可以振荡，而有条件地可以证明它可以在尖锐的边界之间振荡。
We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta-function. Unconditionally this error term can be shown to oscillate, while conditionally it can be shown to oscillate between sharp bounds.
