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March 2019 Note on class number parity of an abelian field of prime conductor, II
Humio Ichimura
Kodai Math. J. 42(1): 99-110 (March 2019). DOI: 10.2996/kmj/1552982508

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.

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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

Information

Published: March 2019
First available in Project Euclid: 19 March 2019

zbMATH: 07081615
MathSciNet: MR3934615
Digital Object Identifier: 10.2996/kmj/1552982508

Rights: Copyright © 2019 Tokyo Institute of Technology, Department of Mathematics

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Vol.42 • No. 1 • March 2019
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