Hostname: page-component-5cf477f64f-fcbfl Total loading time: 0 Render date: 2025-04-03T03:04:21.500Z Has data issue: false hasContentIssue false
  • English
  • Français

On a problem of Ono and quadratic non-residues

Published online by Cambridge University Press:  22 January 2016

Ming-Guang Leu
Ming-Guang Leu*
Affiliation:
Department of Mathematics, The Johns Hopkins University, Baltimore, MD 21218, U.S.A.
*
Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, R. O. C.
Rights & Permissions [Opens in a new window]

Extract

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.

Let k be a quadratic field, Δk the discriminant and Mk the Minkowski constant:

Consider the finite set of prime numbers

There are exactly 8 fields for which Πk = ∅. They make up an exceptional family:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 185 - 198
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[1] Brauer, A., Combinatorial Methods in the Distribution of k-th Power Residues, Combinatorial Mathematics and its Applications, Chapel Hill 1967, 14–37.Google Scholar
[2] Hudson, R. H. and Williams, K. S., On the Least Quadratic Nonresidue of a prime p = 3 (mod 4), J. Reine Angew. Math., 318 (1980), 106–109.Google Scholar
[3] Leu, M.-G., On a Conjecture of Ono on Real Quadratic Fields, Proc. Japan Acad., 63A (1987), 323–326.Google Scholar
[4] Ono, T., A Problem on Quadratic Fields, Proc. Japan Acad., 64A (1988), 78–79.Google Scholar
[5] Rédei, L., Über die Anzahl der Potenzreste mod p im Intervall, 1, Nieuw Arch. Wiskunde, (2) 23 (1950), 150–162.Google Scholar
[6] Stark, H. M., A complete determination of the complex quadratic fields of class-number one, Michigan Math. J., 14 (1967), 1–27.CrossRefGoogle Scholar