Partial sums of the M{ö}bius function

Mathematics – Number Theory

Scientific paper

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11 pages; AIM preprint number 2007-23; Version 2 makes some expository changes

Scientific paper

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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