Accessibility navigation


Generalised prime systems with periodic integer counting function

Downloads

Downloads per month over past year

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

[img] Text - Accepted Version
· Please see our End User Agreement before downloading.

289Kb

To link to this article 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 and Physical Sciences > Department of Mathematics and Statistics
ID Code:23409
Publisher:Institutum Mathematicum - Academia Scientiarum Polona

Download Statistics for this item.

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation