Sampling the Lindel\"of Hypothesis with the Cauchy Random Walk
Probability
2014-02-26 v2 Complex Variables
Number Theory
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.
Cite
@article{arxiv.math/0703693,
title = {Sampling the Lindel\"of Hypothesis with the Cauchy Random Walk},
author = {Mikhail Lifshits and Michel Weber},
journal= {arXiv preprint arXiv:math/0703693},
year = {2014}
}