6
$\begingroup$

I am interested in knowing the parity of the class number of a number field of the shape $L = K(\omega)$, where $\omega$ is a primitive cubic root of unity and $K$ is a totally real field (of class number one). Are there any known criteria on $K$ under which the class number of $L$ is even?

Does anyone know of references related to this question? It looks like P.E. Conner and J. Hurrelbrink's book "Class Number Parity" might have something related to this, but I wasn't able to find an electronic/hard copy of it.

Improve this question
$\endgroup$
1
  • $\begingroup$ You can try to look at H. Ichimura, Refined version of Hass'es Satz 45 on class number parity, Tsukuba J. Math, Vol. 38 No. 2 (2014), 189–199. What is more or less clear is that information on the narrow class number of $K$ is more relevant than the "usual" class number: if the narrow class number is $1$ and there is a unique prime above $3$ in $K$, for instance, then $2\nmid h_L$ as in Theorem 10.4b of Washington's Introduction to cyclotomic fields $\endgroup$
    – Filippo Alberto Edoardo
    Jun 19, 2017 at 22:59

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.