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  • Research Article
  • Open Access

Mean values of multiplicative functions over function fields

  • 1Email author,
  • 2 and
  • 3
Research in Number Theory20151:25

https://doi.org/10.1007/s40993-015-0023-5

  • Received: 29 April 2015
  • Accepted: 28 August 2015
  • Published:

Abstract

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 fields, which display some features that are not present in the integer situation.

Keywords

  • Multiplicative functions
  • Halász’s theorem
  • Function fields

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