MÖBIUS INVERSION AND THE DISTRIBUTION OF PRIMES OF INTEGERS
MARIUS OVERHOLT
A heuristic for the size of the Möbius inverse is obtained by means of matrix algebra, using the spectral
theorem and the concentration of measure phenomenon on high-dimensional spheres. When this heuristic
is applied to the summatory function M (x) of the Möbius function µ, it yields a plausibility argument
in favor of the Riemann Hypothesis. Some computational evidence bearing on this will be presented. It
seems fairly probable that Thomas Jan Stieltjes discovered this approach to Möbius inversion more than
a hundred years ago, while working on his claimed proof of RH (which he never published.)
University of Tromsø, Norway
E-mail address: marius@math.uit.no
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