Abstract
Let K m 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 P m (x) = x 3 − mx 2 − (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 < 1010 for which some prime q ≥ p divides the class numbers h + p of their maximal real subfields Q(ζp)+ (but we did Not find any conterexample to Vandiver’s conjecture!).
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Louboutin, S.R. (2002). Efficient Computation of Class Numbers of Real Abelian Number Fields. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_11
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DOI: https://doi.org/10.1007/3-540-45455-1_11
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