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Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's -rationality conjecture
In this paper we make a series of numerical experiments to support
Greenberg's -rationality conjecture, we present a family of -rational
biquadratic fields and we find new examples of -rational multiquadratic
fields. In the case of multiquadratic and multicubic fields we show that the
conjecture is a consequence of the Cohen-Lenstra-Martinet heuristic and of the
conjecture of Hofmann and Zhang on the -adic regulator, and we bring new
numerical data to support the extensions of these conjectures. We compare the
known algorithmic tools and propose some improvements
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