Values of the Euler phi function not divisible by a prescribed odd prime

dc.creatorMoree, Pieter
dc.date2006-11-16
dc.date.accessioned2026-07-07T07:33:01Z
dc.date.available2026-07-07T07:33:01Z
dc.descriptionLet 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.description20 pages, 2 tables (each of them page filling)
dc.identifierhttps://arxiv.org/abs/math/0611509
dc.identifierhttp://arxiv.org/abs/math/0611509
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119316
dc.subjectNumber Theory
dc.subject11N37; 11Y60
dc.titleValues of the Euler phi function not divisible by a prescribed odd prime
dc.typetext

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