Halasz's theorem for Beurling generalized numbers

Gregory Debruyne,Frederick Maes,Jasson Vindas

arXiv: Number Theory（2020）

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摘要

We show that Halasz’s theorem holds for Beurling numbers under the following two mild hypotheses on the generalized number system: existence of a positive density for the generalized integers and a Chebyshev upper bound for the generalized primes.

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关键词

Halasz theorem,Halasz-Wirsing mean-value theorem,Beurling generalized primes and integers,multiplicative functions,multiplicative arithmetic measures,mean-value vanishing of the Mobius function

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