#### 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.

##### Keywords
p-adic regulator, distribution of p-adic regulators
##### Mathematical Subject Classification 2010
Primary: 11Y40
Secondary: 11K41, 11R20, 11R27
##### Milestones
Received: 2 March 2018
Revised: 13 June 2018
Accepted: 12 September 2018
Published: 13 February 2019
##### Authors
 Tommy Hofmann Fachbereich Mathematik Technische Universität Kaiserslautern Kaiserslautern Germany Yinan Zhang Mathematical Sciences Institute Australian National University Canberra Australia