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Completely multiplicative functions with sum zero over generalised prime systems

Neamah, A. A. (2020) Completely multiplicative functions with sum zero over generalised prime systems. Research in Number Theory, 6 (4). 45. ISSN 2363-9555

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To link to this item DOI: 10.1007/s40993-020-00215-z


CMO 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).

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:94202
Uncontrolled Keywords:Research, Beurling’s generalized primes, Multiplicative functions, 11N80, 11N56


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