Mathematics – Number Theory
Scientific paper
2007-05-05
Mathematics
Number Theory
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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