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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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:23409
Publisher:Institutum Mathematicum - Academia Scientiarum Polona

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