## Tsukuba Journal of Mathematics

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

Humio Ichimura

#### 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

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

#### 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