Let $h_n$ denote the class number of $\Q(2\cos(2\pi/2^{n+2}))$.
Weber proved that $h_n$ is odd for all $n\geq 1$.
We claim that if $\ell$ is a prime number less than $10^7$, then
for all $n\geq 1$, $\ell$ does not divide $h_n$.
Publié le : 2009-05-15
Classification:
Class number,
computation,
11G15,
11R27,
11Y40
@article{1259158432,
author = {Fukuda, Takashi and Komatsu, Keiichi},
title = {Weber's Class Number Problem in the Cyclotomic $\Z\_2$-Extension of $\Q$},
journal = {Experiment. Math.},
volume = {18},
number = {1},
year = {2009},
pages = { 213-222},
language = {en},
url = {http://dml.mathdoc.fr/item/1259158432}
}
Fukuda, Takashi; Komatsu, Keiichi. Weber's Class Number Problem in the Cyclotomic $\Z_2$-Extension of $\Q$. Experiment. Math., Tome 18 (2009) no. 1, pp. 213-222. http://gdmltest.u-ga.fr/item/1259158432/