Chinese Quarterly Journal of Mathematics ›› 2017, Vol. 32 ›› Issue (2): 111-117.doi: 10.13371/j.cnki.chin.q.j.m.2017.02.001

    Next Articles

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

  

  1. 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);

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

CLC Number: