Abstract
For a fixed integer $n \geq 1$, let $p=2n\ell+1$ be a prime number with an odd prime number $\ell$, and let $F=F_{p,\ell}$ be the real abelian field of conductor $p$ and degree $\ell$. We show that the class number $h_F$ of $F$ is odd when 2 remains prime in the real $\ell$th cyclotomic field $\mathbf{Q}(\zeta_{\ell})^+$ and $\ell$ is sufficiently large.
Citation
Humio Ichimura. "Note on class number parity of an abelian field of prime conductor, II." Kodai Math. J. 42 (1) 99 - 110, March 2019. https://doi.org/10.2996/kmj/1552982508