Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T05:36:43.450Z Has data issue: false hasContentIssue false
  • English
  • Français

On plain lattice points whose coordinates are reciprocals modulo a prime

Published online by Cambridge University Press:  22 January 2016

Akio Fujii  and
Yoshiyuki Kitaoka
Akio Fujii
Affiliation:
Department of Mathematics, Rikkyo University, Toshima-ku, Tokyo 171, Japan, fujii@rkmath.rikkyo.ac.jp
Yoshiyuki Kitaoka
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan, kitaokaOmath.nagoya-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 147 , September 1997 , pp. 137 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[1] Dinaburg, E. I. and Sinai, Y. G., Statistics of the solutions of the integral equations ax-by =±1, Funct. Anal. Appl., 24 (1990), 165–171.Google Scholar
[2] Fujii, A., On a problem, of Dinaburg and Sinai, Proc. of Japan Academy, 68A (1992), 198–203.Google Scholar
[3] Hooley, C., Applications of sieve methods to the theory of numbers, Cambridge Univ. Press, 1976.Google Scholar