论文标题
Riemann Zeta函数的随机乘法函数的部分总和和模型的极端价值
Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function
论文作者
论文摘要
我们考虑加权Steinhaus随机乘法函数的部分总和，并将其视为Riemann Zeta函数的模型。我们对该物体的尾巴和高时刻进行描述。使用这些，我们确定了$ t \ log t $独立采样我们总和的最大值，发现这与农民的猜想 - gonek----------------------------》最大程度地符合Riemann Zeta功能。我们还考虑了几乎确定的界限问题。我们确定平方取消和下限水平上的上限，这表明取消程度大得多，我们推测的是符合Euler产品的影响。
We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object. Using these we determine the likely maximum of $T \log T$ independently sampled copies of our sum and find that this is in agreement with a conjecture of Farmer--Gonek--Hughes on the maximum of the Riemann zeta function. We also consider the question of almost sure bounds. We determine upper bounds on the level of squareroot cancellation and lower bounds which suggest a degree of cancellation much greater than this which we speculate is in accordance with the influence of the Euler product.
