论文标题
长dirichlet多项式的条件平均值
Conditional mean values of long Dirichlet polynomials
论文作者
论文摘要
在Riemann假设上有条件地证明了涉及Von Mangoldt函数的各种长dirichlet多项式的平均值的渐近公式。我们的结果避免了使用相关总和估计值，尽管除了Riemann假设外，我们还必须假设我们的Dirichlet多项式具有来自特定类别的权重，该类别的转换足够集中在原点附近。我们还给出了这些长的差异多项式的大偏差估计值。
Conditionally on the Riemann hypothesis we prove asymptotic formulae for mean values of various long Dirichlet polynomials involving the von Mangoldt function. Our results avoid the use of correlation sum estimates although in addition to the Riemann hypothesis we must assume that our Dirichlet polynomials have weights from a specific class whose transforms are sufficiently concentrated near the origin. We also give large deviation estimates for these long Dirichlet polynomials.
