Random Matrix Theory and ζ(1/2+it)

By Jon P Keating, N. Snaith. 2000

815 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a7f63c00882b7c5462005d63f57069579c5d41d1

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The fourth moment of quadratic Dirichlet L-functions over function fields (2016, methodology): “Generally, it is conjectured that ∑∗ 0<d≤D L ( 1 2 , χd k ∼ CkD(logD) k(k+1) 2 , and the precise value of Ck follows from work of Keating and Snaith [20], again using random matrix theory.”
Integral Moments of L‐Functions (2002, background): “either individually (i.e. along the appropriate critical line), or with respect to averages over families. Speciﬁcally, we shall calculate the integral moments of these distributions. KeatingandSnaith[KS1]suggested thatthevalue distribution ofthe Riemannζ-function (or any other principal L-function)”
How to generate random matrices from the classical compact groups (2006, background): “Indeed, the work of Montgomery [11], Odlyzko [12], Katz and Sarnak [6], Keating and Snaith [7, 8] and Rubinstein [13] has shown beyond doubt that the local statistical properties of the”
The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “the non-trivial zeroes of the zeta function behave statistically speaking like the eigenvalues of a large random matrix. This conjectural connection was a motivation in the work of Keating and Snaith [53], who suggested that the statistical behavior of the zeta function should be modelled by the cha”
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “Keating and Snaith [60], [61] opened a new chapter by suggesting unambiguously that the characteristic polynomial Z(M, θ) = n ∏”
Random Matrix Theory and L-Functions at s= 1/2 (2000, methodology): “Following the arguments of [10], the relation between N and Q should arise from equating the mean densities of zeros.”
Fluctuations of eigenvalues and second order Poincaré inequalities (2007, background): “i [1]. Other inﬂuential ideas, sometimes at varying levels of rigor, come from the papers of Costin and Lebowitz [19], Boutet de Monvel, Pastur and Shcherbina [12], Johansson [33], Keating and Snaith [37], Hughes et. al. [30], Soshnikov [48], Israelson [31] and Wieand [52]. The recent works of Ander”
On the extreme values of the Riemann zeta function on random intervals of the critical line (2016, methodology): “ on the pair correlation of zeros of ζ, which have been observed by Dyson to be similar to what we obtain for eigenvalues of random Hermitian or unitary matrices, the conjecture by Keating and Snaith [KS00] on the moments of ζon the critical line, and the limit theorems by Katz and Sarnak [KS99] on ”
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function (2000, background): “Keating and Snaith [38, 39] have pioneered a fresh investigation based on matching zeros at height T to the eigenvalues in Un with n of order log(T ).”