Values of the Euler phi function not divisible by a prescribed odd prime
数论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0611509,
title = {Values of the Euler phi function not divisible by a prescribed odd prime},
author = {Pieter Moree},
journal= {arXiv preprint arXiv:math/0611509},
year = {2007}
}
备注
20 pages, 2 tables (each of them page filling)