Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis

DOI10.1088/1742-5468/ac22fbOpenAlexW3216322276WikidataQ114096194 ScholiaQ114096194MaRDI QIDQ5860328

André Leclair, Giuseppe Mussardo

Publication date: 19 November 2021

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.10336

zbMATH Keywords

Brownian motion

Mathematics Subject Classification ID

Statistical mechanics, structure of matter (82-XX)

Related Items

Phenomenological formula for quantum Hall resistivity based on the Riemann zeta function

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Möbius function is strongly orthogonal to nilsequences
• Supersymmetry and the Möbius inversion function
• The classical theory of zeta and \(L\)-functions.
• Value distribution of \(L\)-functions
• Matrices and the structure of random number sequences
• A consistent test for multivariate normality based on the empirical characteristic function
• A universal statistical test for random bit generators
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Zeros of principal \(L\)-functions and random matrix theory
• The Riemann zeros as spectrum and the Riemann hypothesis
• Transcendental equations satisfied by the individual zeros of Riemann \(\zeta\), Dirichlet and modular \(L\)-functions
• Ergodic properties of square-free numbers
• The Berry–Keating Hamiltonian and the local Riemann hypothesis
• The Möbius function and statistical mechanics
• Disproof of the Mertens conjecture.
• PRIME DIVISORS ARE POISSON DISTRIBUTED
• Number Theory in Science and Communication
• Partial sums of the Möbius function
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• Semiclassical formula for the number variance of the Riemann zeros
• More than two fifths of the zeros of the Riemann zeta function are on the critical line.
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• On the Zeros of Dirichlet L-Functions. I
• Distribution of the number of visits of a random walk
• The Riemann Zeros and Eigenvalue Asymptotics
• Probability Theory
• A pseudo zeta function and the distribution of primes
• Approximate entropy for testing randomness
• Some Riemann Hypotheses from random walks over primes
• On the Order of the Mertens Function
• On the Distribution of Spacings Between Zeros of the Zeta Function
• Linear Statistics of Low-Lying Zeros of L-Functions
• The distribution of the summatory function of the Möbius function
• Elements of the Random Walk
• The Riemann-Siegel expansion for the zeta function: high orders and remainders
• Generalized Riemann hypothesis and stochastic time series
• Generalized Riemann hypothesis, time series and normal distributions
• THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE
• Prime Numbers and Brownian Motion
• A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros
• Jensen polynomials for the Riemann zeta function and other sequences
• Structure and Randomness in the Prime Numbers
• An analysis of variance test for normality (complete samples)
• Equivalents of the Riemann Hypothesis
• The Riemann Hypothesis and Pseudorandom Features of the Mobius Sequence
• On the Distribution of the Two-Sample Cramer-von Mises Criterion
• The zeros of the Riemann zeta-function
• The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions
• Statistics and Prime Numbers
• Some Calculations of the Riemann Zeta-Function
• A Test of Goodness of Fit
• Brownian Motion
• A class of modified \(\zeta\) and \(L\)-functions
• Random matrix theory and \(\zeta(1/2+it)\).
• Low lying zeros of families of \(L\)-functions
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it