Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-1983-0701641-2
MathSciNet review: 701641
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.
  • [5] D. Shanks, "The simplest cubic fields," Math. Comp., v. 28, 1974, pp. 1137-1152. MR 0352049 (50:4537)
  • [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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A50, 12-04, 12A35

Retrieve articles in all journals with MSC: 12A50, 12-04, 12A35


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0701641-2
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society