Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the supplement to the law of biquadratic reciprocity


Author: Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 59 (1976), 19-22
MSC: Primary 10A15
MathSciNet review: 0414468
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A short proof is given of the supplement to the law of biquadratic reciprocity proved by Eisenstein in 1844.


References [Enhancements On Off] (What's this?)

  • [1] G. Eisenstein, (i) Lois de reciprocité, J. Reine Angew. Math. 28 (1844), 53-67. (ii) Einfacher Beweis und Verallgemeinerung des Fundamentaltheorems für die biquadratischen Reste, J. Reine Angew. Math. 28 (1844), 223-245.
  • [2] C. F. Gauss, (i) Theoria residuorum biquadraticorum. I, Göttinger Abh. 6 (1828); (ii) Theoria residuorum biquadraticorum. II, Göttinger Abh. 7 (1832).
  • [3] Helmut Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil II: Reziprozitätsgesetz, Physica-Verlag, Würzburg-Vienna, 1965 (German). MR 0195848
  • [4] C. G. J. Jacobi, Über die Kreisteilung und ihre Anwendung auf die Zahlentheorie, J. Reine Angew. Math. 30 (1846), 166-182.
  • [5] Pierre Kaplan, Démonstration des lois de réciprocité quadratique et biquadratique, J. Fac. Sci. Univ. Tokyo Sect. I 16 (1969), 115–145 (French). MR 0257028
  • [6] H. J. S. Smith, Report on the theory of numbers, Chelsea, New York, 1965.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10A15

Retrieve articles in all journals with MSC: 10A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0414468-4
Keywords: Gaussian integers, biquadratic residues, primary integers, biquadratic reciprocity
Article copyright: © Copyright 1976 American Mathematical Society