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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Cyclic-sixteen class fields for $ {\bf Q}((-p)\sp{1/2})$ by modular arithmetic

Author: Harvey Cohn
Journal: Math. Comp. 33 (1979), 1307-1316
MSC: Primary 16A05
MathSciNet review: 537976
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Abstract: Numerical experiments result in the construction of cyclic-sixteen class fields for $ {\mathbf{Q}}{( - p)^{1/2}}$, p prime $ < 2000$, by radicals involving quadratic and biquadratic parameters. These fields are characterized by rational factorization properties modulo a variable prime; but it suffices to use only three primes selected and checked by computer to verify the class field, if earlier work (jointly with Cooke) on the cyclic-eight class field is utilized.

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

  • [1] Pierre Barrucand and Harvey Cohn, Note on primes of type 𝑥²+32𝑦², class number, and residuacity, J. Reine Angew. Math. 238 (1969), 67–70. MR 0249396 (40 #2641)
  • [1a] Helmut Bauer, Zur Berechnung der 2-Klassenzahl der quadratischen Zahlkörper mit genau zwei verschiedenen Diskriminantenprimteilern, J. Reine Angew. Math. 248 (1971), 42–46 (German). MR 0289453 (44 #6643)
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  • [6] R. LAKEIN, Class Number and Fundamental Unit of Dirichlet Fields With Prime Relative Discriminant. (Unpublished table.)
  • [7] K. S. WILLIAMS, "On the divisibility of the class number of $ {\mathbf{Q}}{( - p)^{1/2}}$ by 16." (Manuscript.)

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PII: S 0025-5718(1979)0537976-5
Article copyright: © Copyright 1979 American Mathematical Society