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

Seah, Eric; Washington, Lawrence C.; Williams, Hugh C.

doi:10.1090/S0025-5718-1983-0701641-2

The calculation of a large cubic class number with an application to real cyclotomic fields
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by Eric Seah, Lawrence C. Washington and Hugh C. Williams PDF

Math. Comp. 41 (1983), 303-305 Request permission

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

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Kenneth F. Ireland and Michael I. Rosen, A classical introduction to modern number theory, Graduate Texts in Mathematics, vol. 84, Springer-Verlag, New York-Berlin, 1982. Revised edition of Elements of number theory. MR 661047
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Astérisque

Daniel Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137–1152. MR 352049, DOI 10.1090/S0025-5718-1974-0352049-8
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