The average order of the Möbius function for Beurling primesNeamah, 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
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1142/s1793042120500517 Abstract/SummaryIn 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.
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