Completely multiplicative functions with sum zero over generalised prime systemsNeamah, A. A. (2020) Completely multiplicative functions with sum zero over generalised prime systems. Research in Number Theory, 6 (4). 45. ISSN 2363-9555
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: 10.1007/s40993-020-00215-z Abstract/SummaryCMO functions multiplicative functions f for which ∑n=1∞f(n)=0. Such functions were first defined and studied by Kahane and Saïas [14]. We generalised these to Beurling prime systems with the aim to investigate the theory of the extended functions and we shall call them CMOP functions. We give some properties and find examples of CMOP functions. In particular, we explore how quickly the partial sum of these classes of functions tends to zero with different generalised prime systems. The findings of this paper may suggest that for all CMOP functions f over N with abscissa 1, we have ∑n≤xn∈Nf(n)=Ω(1x).
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