Averages of ratios of the Riemann zeta-function and correlations of divisor sums
Averages of ratios of the Riemann zeta-function and correlations of divisor sums
复制标题
黎曼 zeta 函数的比率平均值和除数和的相关性
DOI：
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发表时间：
2016
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
非线性出版的文章包含一个显着的数论组成部分，因为该杂志首次成立。我们研究一个线程，关于统计的零点的黎曼zeta函数。我们通过建立黎曼ζ函数的比率猜想和关于莫比乌斯卷积和除数函数相关性的猜想之间的联系来扩展这一点。具体地说，我们证明了比率猜想和算术相关性猜想意味着相同的结果。这为比率猜想提供了新的支持，该猜想以前是通过与随机矩阵理论中的公式类比和启发式方法来激发的。我们的主要定理推广了最近的计算有关的特殊情况下，两个比。
Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.