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The calculation of a large cubic class number with an application to real cyclotomic fields

Authors: Eric Seah, Lawrence C. Washington and Hugh C. Williams
Journal: Math. Comp. 41 (1983), 303-305
MSC: Primary 12A50; Secondary 12-04, 12A35
MathSciNet review: 701641
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Abstract: The class number of the cubic subfield of the pth cyclotomic field is calculated for the prime $ p = 11290018777$. This is used to construct an example where the class number of the pth real cyclotomic field is larger than p.

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

  • [1] G. Cornell & L. Washington, "Class numbers of cyclotomic fields," J. Number Theory. (To appear.) MR 814005 (87d:11079)
  • [2] K. Ireland & M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, New York-Heidelberg-Berlin, 1982. MR 661047 (83g:12001)
  • [3] C. Neild & D. Shanks, "On the 3-rank of quadratic fields and the Euler product," Math. Comp., v. 28, 1974, pp. 279-291. MR 0352042 (50:4530)
  • [4] J. Oesterlé, "Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisée," Astérisque, v. 61, 1979, pp. 165-167.
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  • [6] H. C. Williams & J. Broere, "A computational technique for evaluating $ L(1,\chi )$ and the class number of a real quadratic field," Math. Comp., v. 30, 1976, pp. 887-893. MR 0414522 (54:2623)

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Article copyright: © Copyright 1983 American Mathematical Society

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