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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the class number of relative quadratic fields
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by Charles J. Parry PDF
Math. Comp. 32 (1978), 1261-1270 Request permission

Abstract:

We describe class number relations between certain pairs of algebraic number fields, both of the same degree over the rational numbers. This relationship is discussed in great detail when the common degree is equal to 4. Some numerical results are given in this case.
References
  • Helmut Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern, Abh. Deutsch. Akad. Wiss. Berlin. Math.-Nat. Kl. 1948 (1948), no. 2, 95 pp. (1950) (German). MR 33863
  • Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239
    • E. HECKE, Vorlesungen über die Theorie der algebraischen Zahlen, Leipzig, 1923. C. S. HERZ, Construction of Class Fields, Lecture Notes in Math., vol. 21, Springer-Verlag, Berlin and New York, 1966. I. KAPLANSKY, Fields and Rings, Univ. of Chicago Press, Chicago, Ill., 1977.
  • Tomio Kubota, Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen biquadratischen Zahlkörpers, Nagoya Math. J. 6 (1953), 119–127 (German). MR 59960
  • Charles J. Parry, Real quadratic fields with class numbers divisible by five, Math. Comp. 31 (1977), no. 140, 1019–1029. MR 498483, DOI 10.1090/S0025-5718-1977-0498483-X
  • Charles J. Parry, Units of algebraic numberfields, J. Number Theory 7 (1975), no. 4, 385–388. MR 384752, DOI 10.1016/0022-314X(75)90042-6
    • C. WALTER, Class Number Relations in Algebraic Number Fields, Ph. D. Thesis, University of Cambridge, 1976. C. WALTER, "Kuroda’s class number relation," Acta Arith. (To appear.)
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 1261-1270
  • MSC: Primary 12A50
  • DOI: https://doi.org/10.1090/S0025-5718-1978-0502013-4
  • MathSciNet review: 502013