Probabilistic interpretation of the Möbius function identity and the Riemann Hypothesis

Details Probabilistic interpretation of the Möbius function identity and the Riemann Hypothesis Probabilistic interpretation of the Möbius function identity and the Riemann Hypothesis

2010-02-08

arxiv.org/abs/1002.1682v1

Mathematics

General Mathematics

8 pages

Scientific paper

We obtained the probabilities for the values of the M\"obius function for arbitrary numbers and found that the asymptotic densities of the squarefree integers among the odd and even numbers are $8/\pi^2$ and $4/\pi^2$, respectively. It is determined that statistics of successive outcomes of the M\"obius function for very large squarefree odd and even numbers behaves similar to statistics of heads and tails of two flipping coins. These preliminary results are giving arguments supporting the Riemann Hypothesis. Its plausibility is based on statistical phenomena for integers.

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