Efficient Computation of Class Numbers of Real Abelian Number Fields
نویسنده
چکیده
Let {Km} be a parametrized family of real abelian number fields of known regulators, e.g. the simplest cubic fields associated with the Q-irreducible cubic polynomials Pm(x) = x −mx2 − (m+ 3)x− 1. We develop two methods for computing the class numbers of these Km’s. As a byproduct of our computation, we found 32 cyclotomic fields Q(ζp) of prime conductors p < 10 for which some prime q ≥ p divides the class numbers hp of their maximal real subfields Q(ζp) (but we did not find any conterexample to Vandiver’s conjecture!).
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