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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.
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Contributor : Bernard Host Connect in order to contact the contributor
Submitted on : Wednesday, February 3, 2016 - 8:01:39 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM

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Nikos Frantzikinakis, Bernard Host. Asymptotics for multilinear averages of multiplicative functions. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP), 2016, 161 (1), pp.87-101. ⟨10.1017/S0305004116000116⟩. ⟨hal-01267079⟩



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