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March 2015 Refined version of Hasse's Satz 45 on class number parity
Humio Ichimura
Tsukuba J. Math. 38(2): 189-199 (March 2015). DOI: 10.21099/tkbjm/1429103720

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.

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Humio Ichimura. "Refined version of Hasse's Satz 45 on class number parity." Tsukuba J. Math. 38 (2) 189 - 199, March 2015. https://doi.org/10.21099/tkbjm/1429103720

Information

Published: March 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1325.11111
MathSciNet: MR3336267
Digital Object Identifier: 10.21099/tkbjm/1429103720

Subjects:
Primary: 11R18
Secondary: 11R29

Rights: Copyright © 2015 University of Tsukuba, Institute of Mathematics

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Vol.38 • No. 2 • March 2015
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