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Criteria for cubic and quartic residuacity

Published online by Cambridge University Press:  26 February 2010

Emma Lehmer
Emma Lehmer
Affiliation:
942 Hilldale Avenue, Berkeley 8, Calif., U.S.A.
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Extract

In a short and little known paper, Jacobi [1] gives conditions for the cubic residuacity of small primes q = 2, 3, ..., 37 to a prime p in terms of the quadratic partition

in the form L ≡ ±µM (mod q), and LM ≡ 0 (mod q).

Type
Research Article
Information
Mathematika , Volume 5 , Issue 1 , June 1958 , pp. 20 - 29
Copyright
Copyright © University College London 1958

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References

1.Jacobi, K. G. J., “De residuis cubicis commentatio numerosa”, Jour, für die reine und angew. Math., 2 (1827), 66–69.Google Scholar
2.Cunningham, A. J. C. and Gosset, T., “On 4-tio and 3-bic residuacity tables”, Mess. of Math., 50 (1920), 1–30.Google Scholar
3.Nagell, T., “Sur quelques problèmes dans la théorie des restes quadratiques et cubiques”, Arkiv för Mat., 3 (1956), 211–222.CrossRefGoogle Scholar
4.Jacobsthal, Ernst, “Anwendungen einer Formel aus der Theorie der quadratischen Reste”, Dissertation (Berlin, 1906).Google Scholar
5.Landau, E., “Über die Verteilung der Primideale in den Idealklassen eines algebraisehen Zahlkörpers”, Math. Annalen, 63 (1906), 202.CrossRefGoogle Scholar
6.Kummer, E. E., Jour, für Math., 30 (1846), 107–116.Google Scholar
7.Hasse, Helmut, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraisehen Zahlkürper, Teil II, Reziprozitätsgesetze.Google Scholar
8.Lebesgue, H., “Recherehes sur les nombres”, Jour, de Math., 3 (1838), 113–144.Google Scholar
9.Lehmer, Emma, “Period equations applied to difference sets”, Proc. American Math. Soc., 6 (1955), 433–442.CrossRefGoogle Scholar
10.Mann, H. B., Introd. to algebraic number theory (Graduate School Studies, Math. Series 1, Ohio State University, 1955).Google Scholar