Partial sums of the Möbius function

By Kannan Soundararajan. 2007

52 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

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