Sampling the Lindelöf Hypothesis with the Cauchy Random Walk

Details Sampling the Lindelöf Hypothesis with the Cauchy Random Walk Sampling the Lindelöf Hypothesis with the Cauchy Random Walk

2007-03-23

arxiv.org/abs/math/0703693v2

Proc. London Math. Soc., 2009, 98, 241--270

Mathematics

Probability

Scientific paper

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.

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