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Partial sums of the M{ö}bius function
Published 5 May 2007 in math.NT and math.CA | (0705.0723v2)
Abstract: Assuming the Riemann Hypothesis we establish an upper bound for the sum of the M{\" o}bius function up to $x$. Our method is based on estimating the frequency with which intervals of a given length can contain an unusual number of ordinates of zeros of the Riemann zeta-function.
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