Random Matrix Theory and ζ(1/2+ it)

2000/10/01 by J. P. Keating, Jonathan P. Keating, N. C. Snaith · 25 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics #Conjecture #Connection (principal bundle) #Critical line #Cumulant #Distribution (mathematics) #Eigenvalues and eigenvectors #Fredholm determinant #Gaussian #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Order (exchange) #Physics #Quantum mechanics #Random Matrices and Applications #Random matrix #Riemann hypothesis #Riemann zeta function #Statistics #Unitary matrix #Unitary state

paper · doi:10.1007/s002200000261

crossref issued 2000/10/01 · crossref published 2000/10/01 · crossref published-print 2000/10/01 · openalex publication_date 2000/10/01 · crossref created 2002/10/06 · crossref deposited 2019/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23 · crossref indexed 2026/07/31

Citations

• The Riemann Zeros and Eigenvalue Asymptotics
• Gaussian Fluctuation in Random Matrices
• Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes
• Zeros of principal L-functions and random matrix theory

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• Optimal local law and central limit theorem for β-ensembles
• Rapid computation of L-functions attached to Maass forms
• Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula
• A random matrix model for elliptic curveL-functions of finite conductor
• Maximum of the Characteristic Polynomial of Random Unitary Matrices
• Extreme gaps between eigenvalues of random matrices
• The characteristic polynomial of a random unitary matrix: a probabilistic approach
• Phase Transitions for Products of Characteristic Polynomials under Dyson Brownian Motion
• A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros
• Nonvanishing of twists of -functions attached to Hilbert modular forms
• Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles
• Random matrix theory and discrete moments of the Riemann zeta function
• Spectral statistics of random Toeplitz matrices
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• Moments of zeta and correlations of divisor‐sums: V
• On the maximum of the CβE field
• Linear Statistics of Point Processes via Orthogonal Polynomials
• On the critical points of random matrix characteristic polynomials and of the Riemann ξ-function
• Random matrix ensembles and integrable differential identities
• Symmetric Sextic Freud Weight
• Lindelöf hypothesis [wikipedia]