A generalisation of Euler's totient function

被引:0
作者
Robu, Vlad [1 ]
机构
[1] Univ Bucharest, Fac Math & Informat, Academiei 14, Bucharest, Romania
来源
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE | 2024年 / 67卷 / 04期
关键词
Euler's totient function; Mertens' third theorem; irreducible integer polynomial; asymptotic lower bound; Frobenius density theorem; natural/Dirichlet density;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Euler's totient function, phi(n), which counts how many of 0,1,& mldr;,n-1 are coprime to n, has an explicit asymptotic lower bound of n/logn, modulo some constant. In this note, we generalise phi; given an irreducible integer polynomial P, we define the arithmetic function phi P(n) that counts the amount of numbers among P(0),P(1),& mldr;,P(n-1) that are coprime to n. We also provide an asymptotic lower bound for phi P(n).
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页码:413 / 418
页数:6
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