Moments of zeta and correlations of divisor-sums: I
Moments of zeta and correlations of divisor-sums: I
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zeta 矩和除数和相关性：I
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Keating
中科院分区：
文献类型：
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作者：
B. Conrey;J. Keating
我们使用长狄利克雷多项式和除数相关研究了临界线上黎曼ζ函数的第二和第四矩和位移矩的计算。以前，这种方法在计算超过8的时刻时被证明是不成功的，甚至是启发式的。对第二个和第四个矩的仔细分析说明了问题的本质，并使我们能够确定在这些方法的标准应用中遗漏的术语。
We examine the calculation of the second and fourth moments and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enables us to identify the terms that are missed in the standard application of these methods.