Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496485 | Journal of Number Theory | 2005 | 13 Pages |
Abstract
In this paper, we study generalised prime systems for which both the prime and integer counting functions are asymptotically well-behaved, in the sense that they are approximately li(x) and Ïx, respectively (where Ï is a positive constant), with error terms of order O(xθ1) and O(xθ2) for some θ1,θ2<1. We show that it is impossible to have both θ1 and θ2 less than 12.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Titus W. Hilberdink,