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The average order of the Möbius function for Beurling primes

Neamah, A. A. and Hilberdink, T. W. (2019) The average order of the Möbius function for Beurling primes. International Journal of Number Theory, 16 (5). pp. 1005-1011. ISSN 1793-7310

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To link to this item DOI: 10.1142/s1793042120500517

Abstract/Summary

In this paper, we study the counting functions ψP(x), NP(x) and MP(x) of a generalized prime system N. Here, MP(x) is the partial sum of the Möbius function over N not exceeding x. In particular, we study these when they are asymptotically well-behaved, in the sense that ψP(x)=x+O(xα+ϵ), NP(x)=ρx+O(xβ+ϵ) and MP(x)=O(xγ+ϵ), for some ρ>0 and α,β,γ<1. We show that the two largest of α,β,γ must be equal and at least 12.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:88220
Uncontrolled Keywords:Algebra and Number Theory
Publisher:World Scientific Publishing

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