## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 42, Number 1 (2019), 99-110.

### Note on class number parity of an abelian field of prime conductor, II

#### 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.

#### Article information

**Source**

Kodai Math. J., Volume 42, Number 1 (2019), 99-110.

**Dates**

First available in Project Euclid: 19 March 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1552982508

**Digital Object Identifier**

doi:10.2996/kmj/1552982508

**Mathematical Reviews number (MathSciNet)**

MR3934615

**Zentralblatt MATH identifier**

07081615

#### Citation

Ichimura, Humio. Note on class number parity of an abelian field of prime conductor, II. Kodai Math. J. 42 (2019), no. 1, 99--110. doi:10.2996/kmj/1552982508. https://projecteuclid.org/euclid.kmj/1552982508