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

FENG Bin

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

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 2: 111 - 117

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.02.001

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

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

FENG Bin(1976-), male, native of Xichong, Sichuan, a lecturer of Yangtze Normal University, Ph.D., engages in analytic number theory.

Received date: 2015-12-06

Online published: 2020-10-23

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)；

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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

Cite this article

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

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