Sampling the Lindelöf Hypothesis with the Cauchy Random Walk
نویسنده
چکیده
admits a meromorphic continuation to the entire complex plane, with the unique and simple pole of residue 1 at s = 1. In the half-plane {s : Rs ≤ 0}, the Riemann zeta function has simple zeros at −2,−4,−6, . . ., and only at these points which are called trivial zeros. There exist also non-trivial zeros in the band {s : 0 < Rs < 1}. We refer for these basic facts for instance to [Bl] (Propositions IV.10 & IV.11, p.84). Two great conjectures are related to the behavior of ζ(s). The Riemann Hypothesis (RH) asserts that all non-trivial zeros of the function ζ have abscissa 12 , while Lindelöf Hypothesis (LH) claims that
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