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February 2010 Divisibility of class numbers of non-normal totally real cubic number fields
Jungyun Lee
Proc. Japan Acad. Ser. A Math. Sci. 86(2): 38-40 (February 2010). DOI: 10.3792/pjaa.86.38

Abstract

In this paper, we consider a family of cubic fields $\{K_m\}_{m\geq4}$ associated to the irreducible cubic polynomials $P_m(x)=x^3-mx^2-(m+1)x-1,\,\,\,(m\geq4).$ We prove that there are infinitely many $\{K_m\}_{m\geq4}$'s whose class numbers are divisible by a given integer n. From this, we find that there are infinitely many non-normal totally real cubic fields with class number divisible by any given integer n.

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Jungyun Lee. "Divisibility of class numbers of non-normal totally real cubic number fields." Proc. Japan Acad. Ser. A Math. Sci. 86 (2) 38 - 40, February 2010. https://doi.org/10.3792/pjaa.86.38

Information

Published: February 2010
First available in Project Euclid: 1 February 2010

zbMATH: 1187.11041
MathSciNet: MR2590188
Digital Object Identifier: 10.3792/pjaa.86.38

Subjects:
Primary: 11R29 , 11R80

Keywords: Class number , totally real cubic fields

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 2 • February 2010
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