Skip to Main content Skip to Navigation
Journal articles

Asymptotics for multilinear averages of multiplicative functions

Abstract : A celebrated result of Hal\'asz describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions providing similar asymptotics, thus verifying a two dimensional variant of a conjecture of Elliott. As a consequence, we get several convergence results for such multilinear expressions, one of which generalizes a well known convergence result of Wirsing. The key ingredients are a recent structural result for bounded multiplicative functions proved by the authors and the mean value theorem of Hal\'asz.
Document type :
Journal articles
Complete list of metadata
Contributor : Bernard Host Connect in order to contact the contributor
Submitted on : Wednesday, February 3, 2016 - 8:01:39 PM
Last modification on : Wednesday, November 3, 2021 - 7:15:21 AM

Links full text


  • HAL Id : hal-01267079, version 1
  • ARXIV : 1502.02646


Nikos Frantzikinakis, Bernard Host. Asymptotics for multilinear averages of multiplicative functions. Math. Proc. Cambridge Philos. Soc., 2016, 161 (1), pp.87--101. ⟨hal-01267079⟩



Record views