Divisibility of class numbers of non-normal totally real cubic number fields

Divisibility of class numbers of non-normal totally real cubic number fields

Jungyun Lee

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 2 (2010), 38-40.

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.

Primary Subjects: 11R29, 11R80

Keywords: Class number; totally real cubic fields

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1265033220
Digital Object Identifier: doi:10.3792/pjaa.86.38
Zentralblatt MATH identifier: 05690873
Mathematical Reviews number (MathSciNet): MR2590188

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References

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Mathematical Reviews (MathSciNet): MR1875340

Zentralblatt MATH: 0997.11093

Digital Object Identifier: doi:10.1007/s229-001-8025-7

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Digital Object Identifier: doi:10.1016/0022-314X(91)90032-7

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