Divisibility of class numbers of non-normal totally real cubic number fields. (English) Zbl 1187.11041

Author’s summary: We consider a family of cubic fields \(\{K_m\}_{m\geq 4}\) 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 \(\{K_m\}_{m\geq 4}\)’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 \(n\).


11R29 Class numbers, class groups, discriminants
11R80 Totally real fields
Full Text: DOI


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