Roots of the derivative of the Riemann-zeta function and of characteristic polynomials
Roots of the derivative of the Riemann-zeta function and of characteristic polynomials
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DOI：
10.1088/0951-7715/23/10/014
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发表时间：
2010-02
期刊：
影响因子：
1.7
通讯作者：
Eduardo Dueñez;D. Farmer;S. Froehlich;C. Hughes;F. Mezzadri;T. Phan
中科院分区：
文献类型：
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作者：
Eduardo Dueñez;D. Farmer;S. Froehlich;C. Hughes;F. Mezzadri;T. Phan
我们调查的Riemann-zeta函数的导数的零点的水平分布，并比较这与随机酉矩阵的特征多项式的导数的零点的径向分布。这两种情况都显示出令人惊讶的双峰分布，这还有待解释。我们通过例子表明，双峰是一种普遍现象。对于酉矩阵的情况下，我们证明了一个猜想的Mezzadri关于领导秩序的行为，我们表明，同样的如下随机矩阵的zeta函数的零点。
We investigate the horizontal distribution of zeros of the derivative of the Riemann-zeta function and compare this with the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a surprising bimodal distribution which is yet to be explained. We show by example that the bimodality is a general phenomenon. For the unitary matrix case we prove a conjecture of Mezzadri concerning the leading order behaviour, and we show that the same follows from the random matrix conjectures for the zeros of the zeta function.