Sampling the Lindelöf Hypothesis with the Cauchy Random Walk

Abstract

We study the behavior of the Riemann zeta function on the critical line when the imaginary part of the argument is sampled by the Cauchy random walk. We develop a complete second order theory for the corresponding system of random variables and show that it behaves almost like a system of non-correlated variables. Exploiting this fact in relation with known criteria for almost sure convergence allows to investigate its almost sure asymptotic behavior.

References in corpus (1)

• The modified Mellin transform of powers of the zeta-function

Cited by in corpus (8)

• An ergodic value distribution of certain meromorphic functions
• Dirichlet polynomials: some old and recent results, and their interplay in number theory
• Note on Prime Gaps and Zero Spacings
• On good universality and the Riemann hypothesis
• An estimate of the second moment of a sampling of the Riemann zeta function on the critical line
• Limit Theorems for a class of unbounded observables with an application to "Sampling the Lindelöf hypothesis"
• Errata and Addenda to Mathematical Constants
• A complement to a recent paper on some infinite sums with the zeta values