Randomness of Mobius coefficents and brownian motion: growth of the Mertens function and the Riemann Hypothesis
Giuseppe Mussardo,
Andre LeClair
Abstract:The validity of the Riemann Hypothesis (RH) on the location of the non-trivial zeros of the Riemann ζ-function is directly related to the growth of the Mertens function M (x) = x k=1 µ(k), where µ(k) is the Möbius coefficient of the integer k: the RH is indeed true if the Mertens function goes asymptotically as M (x) x 1/2+ . We show that this behavior can be established on the basis of a new probabilistic approach based on the global properties of Mertens function. To this aim, we focus the attention on the s… Show more
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