Euler函数值在算术级数中的分布

doi:10.13371/j.cnki.chin.q.j.m.2017.02.001

数学季刊 ›› 2017, Vol. 32 ›› Issue (2): 111-117.doi: 10.13371/j.cnki.chin.q.j.m.2017.02.001

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Euler函数值在算术级数中的分布

School of Mathematics Sciences, Shanghai Jiaotong University. College of Mathematics and Statistics, Yangtze Normal University

收稿日期:2015-12-06 出版日期:2017-06-30 发布日期:2020-10-23
作者简介:FENG Bin(1976-), male, native of Xichong, Sichuan, a lecturer of Yangtze Normal University, Ph.D., engages in analytic number theory.
基金资助:
Supported by the National Natural Science Foundation of China(11271249)； Supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission(1601213)； Supported by the Scientific Research Program of Yangtze Normal University(2012XJYBO31)；

On the Distribution of Values of Euler's Function over Integers in Arithmetic Progressions

School of Mathematics Sciences, Shanghai Jiaotong University. College of Mathematics and Statistics, Yangtze Normal University

Received:2015-12-06 Online:2017-06-30 Published:2020-10-23
About author:FENG Bin(1976-), male, native of Xichong, Sichuan, a lecturer of Yangtze Normal University, Ph.D., engages in analytic number theory.
Supported by:
Supported by the National Natural Science Foundation of China(11271249)； Supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission(1601213)； Supported by the Scientific Research Program of Yangtze Normal University(2012XJYBO31)；

摘要/Abstract

摘要： Let φ（n） denote the Euler-totient function, we study the distribution of solutions of φ（n） ≤ x in arithmetic progressions, where n ≡ l（mod q） and an asymptotic formula was obtained by Perron formula.

关键词: Perron formula, Euler-totient function, arithmetic progressions

Abstract: Let φ（n） denote the Euler-totient function, we study the distribution of solutions of φ（n） ≤ x in arithmetic progressions, where n ≡ l（mod q） and an asymptotic formula was obtained by Perron formula.

Key words: Perron formula, Euler-totient function, arithmetic progressions

中图分类号:

O174.6

冯彬.

Euler函数值在算术级数中的分布

[J]. 数学季刊, 2017, 32(2): 111-117.

FENG Bin. On the Distribution of Values of Euler's Function over Integers in Arithmetic Progressions[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(2): 111-117.

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[2]	张金良, 张令元, 王明亮. Konopelchenko-Dubrovsky方程的周期解[J]. 数学季刊, 2005, 20(1): 72-78.

Euler函数值在算术级数中的分布

On the Distribution of Values of Euler's Function over Integers in Arithmetic Progressions

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