An explicit formula for the fundamental units of a real pure sextic number field and its Galois closure.
Ken Nakamula
Source: Pacific J. Math. Volume 83, Number 2
(1979), 463-471.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102784522
Zentralblatt MATH identifier: 0413.12005
Zentralblatt MATH identifier: 0387.12004
Mathematical Reviews number (MathSciNet): MR557945
References
[1] A. Brumer, On the group of units of an absolutely cyclic number field ofprime degree, J. Math. Soc. Japan, 21 (1969),357-358.
Mathematical Reviews (MathSciNet): MR39:5510
Zentralblatt MATH: 0188.35301
[2] G. Degert, Uber die Bestimmungder Grundeinheitgewisserreelquadratischer Zahlkrper, Abh. Math. Sem. Hamburg, 22 (1958), 92-97.
Mathematical Reviews (MathSciNet): MR19:1164d
Zentralblatt MATH: 0079.05803
[3] K. Iimura, On the unit groups of certain sextic number fields, (to apper in Abh. Math. Sem. Hamburg, 50).
Mathematical Reviews (MathSciNet): MR82f:12007
Zentralblatt MATH: 0416.12002
[4] S. -K. Kuroda, Uber den Dirichletschen Krper, J. Fac. Sci. Univ. Tokyo, 4 (1943), 383-406.
Mathematical Reviews (MathSciNet): MR9:12f
Zentralblatt MATH: 0061.05901
[5] T. Nagell, Zur Arithmetik der Polynome, Abh. Math. Sem. Hamburg, 1 (1922), 174-194.
Zentralblatt MATH: 0079.06305
[6] T. Nagell, Solution complete de quelques equations cubiques a deuxindeterminees, J. Math. Pures Appl., 4 (1925), 209-270.
[7] K. Nakamula, On the group of units of a nongalois quartic or sextic number field, (to appear).
Mathematical Reviews (MathSciNet): MR81h:12004
Zentralblatt MATH: 0471.12005
[8] H. -J. Stender, Uber die Einheitengruppeder reinen algebraischenZahlkrpern sechsten Grades, J. Reine Angew. Math., 268/269 (1974), 78-93.
Mathematical Reviews (MathSciNet): MR50:2121
Zentralblatt MATH: 0289.12005
[9] H. -J. Stender, Eine Formel fur Grundeinheitenin reinen algebraischenZahlkbrpern dritten, vierten und sechsten Grades, J. Numb. Th., 7 (1975), 235-250.
Mathematical Reviews (MathSciNet): MR51:5552
Zentralblatt MATH: 0308.12001
[10] H. -J. Stender, Lsbare Gleichungen axn --by71 --c und Grundeinheitenfureinige algebraische Zahlkrper vom Grade n,%=.3,4,6,J. Reine Angew. Math., 290 (1977), 24-62.
Mathematical Reviews (MathSciNet): MR57:12455
[11] H. Yokoi, On real quadratic fields containing units with norm -1, Nagoya Math. J., 33 (1968), 139-152.
Mathematical Reviews (MathSciNet): MR38:2124
Zentralblatt MATH: 0167.04401
[12] H. Yokoi, On the fundamental unit of real quadratic fields with norm 1, J. Number Theory, 2 (1970), 106-115.
Mathematical Reviews (MathSciNet): MR40:5572
Zentralblatt MATH: 0201.05703
[13] H. Yokoi, The diophantine equation xz + dyB=l and the fundamentalunit of a real pure cubic field Q( ^~d), J. Reine Angew. Math., 268/269 (1974), 174-179.
Mathematical Reviews (MathSciNet): MR50:2122
Zentralblatt MATH: 0294.12003
Pacific Journal of Mathematics