Generalised prime systems with periodic integer counting function

Hilberdink, T. (2012) Generalised prime systems with periodic integer counting function. Acta Arithmetica, 152 (3). pp. 217-241. ISSN 1730-6264 doi: 10.4064/aa152-3-1

Abstract/Summary

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/23409
Identification Number/DOI	10.4064/aa152-3-1
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Institutum Mathematicum - Academia Scientiarum Polona
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