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Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's p-rationality conjecture

Abstract : 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.
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Submitted on : Wednesday, December 18, 2019 - 12:32:32 PM
Last modification on : Friday, January 21, 2022 - 3:19:54 AM
Long-term archiving on: : Thursday, March 19, 2020 - 7:35:30 PM

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  • HAL Id : hal-01534050, version 3

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Razvan Barbulescu, Jishnu Ray. Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's p-rationality conjecture. Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2020, 32 (1), pp.159-177. ⟨hal-01534050v3⟩

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