منابع مشابه
Riemann zeros and random matrix theory
In the past dozen years random matrix theory has become a useful tool for conjecturing answers to old and important questions in number theory. It was through the Riemann zeta function that the connection with random matrix theory was first made in the 1970s, and although there has also been much recent work concerning other varieties of L-functions, this article will concentrate on the zeta fu...
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By looking at the average behavior (n-level density) of the low-lying zeros of certain families of L-functions, we find evidence, as predicted by function field analogs, in favor of a spectral interpretation of the nontrivial zeros in terms of the classical compact groups.
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Abstract. We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N × N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function ζ(s), this is expected to be an accurate description for the horizontal distribution of the zeros of ζ (s) to the right of ...
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Hilbert and Pólya put forward the idea that the zeros of the Riemann zeta function may have a spectral origin : the values of tn such that 1 2 + itn is a non trivial zero of ζ might be the eigenvalues of a self-adjoint operator. This would imply the Riemann Hypothesis. From the perspective of Physics one might go further and consider the possibility that the operator in question corresponds to ...
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ژورنال
عنوان ژورنال: Milan Journal of Mathematics
سال: 2010
ISSN: 1424-9286,1424-9294
DOI: 10.1007/s00032-010-0114-7