On a Restricted Divisor Problem

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Authors

  • Jun Furuya
     Department of Integrated Human Sciences (Mathematics), Hamamatsu University School of Medicine, Handayama 1-20-1, Hamamatsu, Shizuoka, 431-3192 ,JP
  • Makoto Minamide
     Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512 ,JP
  • Yoshio Tanigawa
     Graduate School of Mathematics, Nagoya University, Furo-Cho, Nagoya, 464-8602 ,JP

Keywords:

The Dirichlet Divisor Problem, Mean Square, Chowla and Walum's Expression.

Abstract

Let 0 < α < 1/2 and let dα(n) be the number of positive divisors k of n such that nα ≤ k ≤ n1-α, which we call a restricted divisor function. In the case α = 1/N (N ∈ N) we derive an asymptotic representation of Σn≤xdα(n). Furthermore we study the mean square of Pα(x) = Σl≤xαφ (x/l), which seems to be a natural object in the case of a restricted divisor problem.

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Published

2016-12-01

How to Cite

Furuya, J., Minamide, M., & Tanigawa, Y. (2016). On a Restricted Divisor Problem. The Journal of the Indian Mathematical Society, 83(3-4), 269–287. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/6609

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 Jun Furuya, Makoto Minamide, Yoshio Tanigawa

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

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