Multiplicative functions in short intervals

@inproceedings{Matomaki2015MultiplicativeFI,
  title={Multiplicative functions in short intervals},
  author={Kaisa Matomaki and Maksym Radziwill},
  year={2015}
}
We introduce a general result relating “short averages” of a multiplicative function to “long averages” which are well understood. This result has several consequences. First, for the Möbius function we show that there are cancellations in the sum of μ(n) in almost all intervals of the form [x, x+ψ(x)] with ψ(x)→∞ arbitrarily slowly. This goes beyond what was previously known conditionally on the Density Hypothesis or the stronger Riemann Hypothesis. Second, we settle the long-standing… CONTINUE READING

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