With an Application to Real Cyclotomic Fields - Semantic Scholar
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With an Application to Real Cyclotomic Fields - Semantic Scholar
By Eric Seah, Lawrence C. Washington* and Hugh C. Williams**. Abstract. The class number of the cubic subfield of the pth cyclotomic field is calculated for.
mathematics
volume july
of computation
41, number
1983. pages
163
303-305
The Calculation of a Large Cubic Class Number
With an Application to Real Cyclotomic Fields By Eric Seah, Lawrence C. Washington* and Hugh C. Williams** 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.
In a recent paper [1], it is shown that if the Generalized Riemann Hypothesis
holds, then hp > p for the prime p = 11290018777.Here hp is the class number of Q(cos(27r/p)), the maximal real subfield of the pth cyclotomic field. In the present note we show that the GRH is not needed, so the result holds unconditionally. It is a conjecture of Vandiver, with important consequences for Fermat's Last Theorem and the theory of cyclotomic fields, that p never divides hp . It had been suggested that perhaps hp
