arxiv: 1701.00340 · v1 · pith:E4DNIR3Rnew · submitted 2017-01-02 · 🧮 math.NT

Valuations of p-adic regulators of cyclic cubic fields

Tommy Hofmann , Yinan Zhang This is my paper

classification 🧮 math.NT

keywords adiccubiccyclicregulatorsdistributionfieldsmatrixmodel

0 comments p. Extension

Add this Pith Number to your LaTeX paper

\usepackage{pith}
\pithnumber{E4DNIR3R}

Prints a linked pith:E4DNIR3R badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more

read the original abstract

We compute the $p$-adic regulator of cyclic cubic extensions of $\mathbb Q$ with discriminant up to $10^{16}$ for $3<p<100$, and observe the distribution of the $p$-adic valuation of the regulators. We find that for almost all primes, the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions. Based on this random matrix model, a conjecture on the distribution of the valuations of $p$-adic regulators of cyclic cubic fields is stated.

This paper has not been read by Pith yet.

Valuations of p-adic regulators of cyclic cubic fields

discussion (0)