Values of the Euler phi function not divisible by a prescribed odd prime
| dc.creator | Moree, Pieter | |
| dc.date | 2006-11-16 | |
| dc.date.accessioned | 2026-07-07T07:33:01Z | |
| dc.date.available | 2026-07-07T07:33:01Z | |
| dc.description | Let phi denote Euler's phi function. For a fixed odd prime we give an asymptotic series expansion in the sense of Poincare for the number E_q(x) of n<=x such that q does not divide phi(n). Thereby we improve on a recent theorem of B.K. Spearman and K.S. Williams [Ark. Mat. 44 (2006), 166-181]. Furthermore we resolve, under the Generalized Riemann Hypothesis, which of two approximations to E_q(x) is asymptotically superior using recent results of Y. Ihara on the Euler-Kronecker constant of a number field. | |
| dc.description | 20 pages, 2 tables (each of them page filling) | |
| dc.identifier | https://arxiv.org/abs/math/0611509 | |
| dc.identifier | http://arxiv.org/abs/math/0611509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119316 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 11Y60 | |
| dc.title | Values of the Euler phi function not divisible by a prescribed odd prime | |
| dc.type | text |