Kodai Mathematical Journal

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

Humio Ichimura

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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.

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

First available in Project Euclid: 19 March 2019

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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

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