紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2013, 50(3), p. 687-713

ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2013-09

The indicator function of the set of k-th power free integers is naturally extended to a random variable X^(k)(・) on (Z^, λ), where Z^ is the ring of finite integral adeles and λ is the Haar probability measure. In the previous paper, the first author noted the strong law of large numbers for {X^(k)(・ + n)}_n^∞, and showed the asymptotics: E^λ[(Y_N^(k))^2] ≍ 1 as N → 1, where Y_N^(k)(x) := N^(-1/2k) Σ_{n=1}^N (X^(k)(x + n) - 1/ξ(k)) . In the present paper, we prove the convergence of E^λ[(Y_N(k))^22]. For this, we present a general proposition of analytic number theory, and give a proof to this.

10.18910/26013

26013

ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II

Osaka University and Osaka City University, Departments of Mathematics

英語

2013-09

Osaka Journal of Mathematics

50

3

687

713

https://hdl.handle.net/11094/26013

10.18910/26013

https://doi.org/10.18910/26013