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

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Jungyun Lee¹ 

[1] ASARC Department of Mathematical Sciences KAIST 335 Gwahangno

关键词: Class number;    totally real cubic elds.;   

DOI  :  10.3792/pjaa.86.38

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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 .

【 授权许可】

Unknown