Tsukuba Journal of Mathematics

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

Humio Ichimura

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Abstract

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

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

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1429103720

Digital Object Identifier
doi:10.21099/tkbjm/1429103720

Mathematical Reviews number (MathSciNet)
MR3336267

Zentralblatt MATH identifier
1325.11111

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

Keywords
Class number parity abelian field reflection argument

Citation

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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