Vol. 2, 2019

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Cyclic extensions of prime degree and their $p$-adic regulators

Tommy Hofmann and Yinan Zhang

Vol. 2 (2019), No. 1, 311–323
Abstract

We present a conjecture on the distribution of the valuations of $p$-adic regulators of cyclic extensions of $ℚ$ of odd prime degree. This is based on the observation of computational data of $p$-adic regulators of the 5 521 222 cyclic quintic and 329 708 cyclic septic extensions of $ℚ$ for $2 with discriminant up to $5×1{0}^{31}$ and $1{0}^{42}$ respectively, and noting that the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions.