Zeros of principal L-functions and random matrix theory

1996/01/01 by Zeév Rudnick, Peter Sarnak · 25 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Random Matrices and Applications

paper · doi:10.1215/s0012-7094-96-08115-6

Citations

• Toeplitz matrices, translation kernels and a related problem in probability theory
• On Euler Products and the Classification of Automorphic Representations I
• On Certain L-Functions
• Rankin-Selberg Convolutions

Cited by

• Zeros of Polynomials in Derivatives of Automorphic L-functions
• Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks
• A class number formula for Picard modular surfaces
• Discorrelation of multiplicative functions with nilsequences and its application on coefficients of automorphic L-functions
• On the absolute convergence of the spectral side of the Arthur trace\n formula for GL(n)
• The Set of Prime Numbers
• On the local Langlands correspondence for quasi-split even orthogonal groups
• Formes automorphes et voisins de Kneser des réseaux de Niemeier
• Random Matrices, Intrinsic Freeness, and Sharp Non-Asymptotic Inequalities
• The Riemann-zeta function on vertical arithmetic progressions
• The highest lowest zero and other applications of positivity
• Strong multiplicity one for the Selberg class
• Universality for mathematical and physical systems
• Non-vanishing of L-functions, the Ramanujan conjecture, and families of\n Hecke characters
• Integral moments of L-functions
• Centered Moments of Weighted One-Level Densities of GL(2) L-Functions
• The correlations of Farey fractions
• Prime pairs and Zeta's zeros
• Low-lying zeros of Hilbert modular L-functions weighted by powers of central L-values
• Joint value distribution of L-functions on the critical line
• Low-lying Zeros of Number Field L-functions
• The second moment of Dirichlet twists of a \textrmGL₄ automorphic L-function
• The second moment theory of families of L-functions
• Selberg orthogonality for half-integral weight modular forms
• A Combinatorial Approach to Mixed Ratios of Characteristic Polynomials