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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/88220
Identification Number/DOI	10.1142/s1793042120500517
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Algebra and Number Theory
Publisher	World Scientific Publishing
Download/View statistics	View download statistics for this item