机构:
Univ Bucharest, Fac Math & Informat, Academiei 14, Bucharest, RomaniaUniv Bucharest, Fac Math & Informat, Academiei 14, Bucharest, Romania
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).
引用
收藏
页码:413 / 418
页数:6
相关论文
共 6 条
[1]
ANDREESCU T., 2017, Number Theory: Concepts and Problems