Kodai Mathematical Journal

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

Humio Ichimura

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

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