Symmetry transitions in random matrix theory \& \(L\)-functions

DOI10.1007/s00220-008-0483-8zbMath1170.11029OpenAlexW2051693748MaRDI QIDQ1006869

B. E. Odgers, Jonathan P. Keating

Publication date: 26 March 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-008-0483-8

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Other Dirichlet series and zeta functions (11M41) Moment problems (44A60)

Related Items

Sums of divisor functions and von Mangoldt convolutions in \(\mathbb{F}_q [T\) leading to symplectic distributions], Maxima of log-correlated fields: some recent developments*, Conjectures for the integral moments and ratios of \(L\)-functions over function fields, Random matrix theory and moments of moments of L-functions, Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals], Correlation of shifted values of \(L\)-functions in the hyperelliptic ensemble, The integral moments and ratios of quadratic Dirichlet \(L\)-functions over monic irreducible polynomials in \(\mathbb{F}_q [T\)], Moments of random multiplicative functions. II: High moments, Angles of Gaussian primes, On the moments of the moments of the characteristic polynomials of random unitary matrices

Cites Work

• A hybrid Euler-Hadamard product for the Riemann zeta function
• Lower order terms in the full moment conjecture for the Riemann zeta function
• Bounds for automorphic \(L\)-functions
• Bounds for automorphic \(L\)-functions. II
• Real zeros of quadratic Dirichlet \(L\)-functions
• Autocorrelation of random matrix polynomials
• Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• The critical order of vanishing of automorphic \(L\)-functions with large level
• Zeros of principal \(L\)-functions and random matrix theory
• Statistical Theory of the Energy Levels of Complex Systems. I
• The Riemann Zeros and Eigenvalue Asymptotics
• Random matrix theory and the Riemann zeros II:n-point correlations
• Random matrices andL-functions
• Mock-Gaussian behaviour for linear statistics of classical compact groups
• Random matrix theory and the Riemann zeros. I. Three- and four-point correlations
• Applications of theL-functions ratios conjectures
• Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation
• On the mean values of Dirichlet L -functions
• Integral moments of L-functions
• On the mean values of L -functions in orthogonal and symplectic families
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros
• Random matrix theory and \(L\)-functions at \(s=1/2\).
• Random matrix theory and \(\zeta(1/2+it)\).
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item