Mean values of multiplicative functions over function fields

@article{Granville2015MeanVO,
  title={Mean values of multiplicative functions over function fields},
  author={Andrew Granville and Adam J. Harper and Kannan Soundararajan},
  journal={Research in Number Theory},
  year={2015},
  volume={1},
  pages={1-18}
}
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function… CONTINUE READING

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