Partial Sums of the Möbius Function
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چکیده
(1) M(x) ≪ x 1 2. Conversely, the estimate M(x) ≪ x 12+ǫ implies, by partial summation, the convergence of the series ∑∞ n=1 μ(n)n −s = 1/ζ(s) for any σ > 1/2, and therefore RH. Subsequently, E. Landau [5] showed that, assuming RH, (1) is valid with ǫ ≪ log log log x/ log log x, and E.C. Titchmarsh [13] improved this to ǫ ≪ 1/ log log x. H. Maier and H.L. Montgomery [7] obtained a substantial improvement over these results, and established that
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تاریخ انتشار 2007