Tsukuba Journal of Mathematics

Refined version of Hasse's Satz 45 on class number parity

Humio Ichimura

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For an imaginary abelian field $K$, Hasse [3, Satz 45] obtained a criterion for the relative class number to be odd in terms of the narrow class number of the maximal real subfield $K^+$ and the prime numbers which ramify in $K$, by using the analytic class number formula. In [4], we gave a refined version (= "$\Delta$-decomposed version") of Satz 45 by an algebraic method. In this paper, we give one more algebraic proof of the refined version.

Article information

Tsukuba J. Math., Volume 38, Number 2 (2015), 189-199.

First available in Project Euclid: 15 April 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R18: Cyclotomic extensions
Secondary: 11R29: Class numbers, class groups, discriminants

Class number parity abelian field reflection argument


Ichimura, Humio. Refined version of Hasse's Satz 45 on class number parity. Tsukuba J. Math. 38 (2015), no. 2, 189--199. doi:10.21099/tkbjm/1429103720. https://projecteuclid.org/euclid.tkbjm/1429103720

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