On the imaginary bicyclic biquadratic fields with class-number $2$
HTML articles powered by AMS MathViewer
- by D. A. Buell, H. C. Williams and K. S. Williams PDF
- Math. Comp. 31 (1977), 1034-1042 Request permission
Abstract:
Assuming that the list of imaginary quadratic number fields of class-number 4 is complete, a determination is made of all imaginary bicyclic biquadratic number fields of class-number 2.References
- Pierre Barrucand and Harvey Cohn, A rational genus, class number divisibility, and unit theory for pure cubic fields, J. Number Theory 2 (1970), 7–21. MR 249398, DOI 10.1016/0022-314X(70)90003-X
- Ezra Brown and Charles J. Parry, The imaginary bicyclic biquadratic fields with class-number $1$, J. Reine Angew. Math. 266 (1974), 118–120. MR 340219, DOI 10.1515/crll.1974.266.118
- Duncan A. Buell, Class groups of quadratic fields, Math. Comp. 30 (1976), no. 135, 610–623. MR 404205, DOI 10.1090/S0025-5718-1976-0404205-X
- Duncan A. Buell, Small class numbers and extreme values of $L$-functions of quadratic fields, Math. Comp. 31 (1977), no. 139, 786–796. MR 439802, DOI 10.1090/S0025-5718-1977-0439802-X M. N. GRAS & G. GRAS, Nombre de Classes des Corps Quadratiques Réels $Q(\sqrt m )$, $m < 10000$, Institut de Mathématiques Pures, Université Scientifique et Médicale de Grenoble, 1971/72.
- G. Herglotz, Über einen Dirichletschen Satz, Math. Z. 12 (1922), no. 1, 255–261 (German). MR 1544516, DOI 10.1007/BF01482079 E. L. INCE, Cycles of Reduced Ideals in Quadratic Fields, Mathematical Tables, vol. IV, British Association for the Advancement of Science, London, 1934.
- Tomio Kubota, Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen biquadratischen Zahlkörpers, Nagoya Math. J. 6 (1953), 119–127 (German). MR 59960
- Sigekatu Kuroda, Über den Dirichletschen Körper, J. Fac. Sci. Imp. Univ. Tokyo Sect. I. 4 (1943), 383–406 (German). MR 0021031
- H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1973/74), 529–542. MR 357373, DOI 10.4064/aa-24-5-529-542
- H. M. Stark, A complete determination of the complex quadratic fields of class-number one, Michigan Math. J. 14 (1967), 1–27. MR 222050
- H. M. Stark, On complex quadratic fields wth class-number two, Math. Comp. 29 (1975), 289–302. MR 369313, DOI 10.1090/S0025-5718-1975-0369313-X
- H. C. Williams and J. Broere, A computational technique for evaluating $L(1,\chi )$ and the class number of a real quadratic field, Math. Comp. 30 (1976), no. 136, 887–893. MR 414522, DOI 10.1090/S0025-5718-1976-0414522-5
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 1034-1042
- MSC: Primary 12A30; Secondary 12A50
- DOI: https://doi.org/10.1090/S0025-5718-1977-0441914-1
- MathSciNet review: 0441914