Numerical verification of the Cohen–Lenstra–Martinet heuristics and of Greenberg’s p -rationality conjecture
Razvan Barbulescu, Jishnu Ray · Journal de Théorie des Nombres de Bordeaux · 2020
In this paper we make a series of numerical experiments to support Greenberg’s p -rationality conjecture, we present a family of p -rational biquadratic fields and we find new examples of p -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 p -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.