Scarowsky, Manny; Boyarsky, Abraham On the computation of the class numbers of some cubic fields. (English) Zbl 0626.12005 Int. J. Math. Math. Sci. 9, 797-800 (1986). Let \(f(x)=x^ 3+12Ax-12\) with \(A>0\). Class numbers are calculated for the cubic fields generated by the unique real root of the equations \(f(x)=0\), where A takes the values \(1\leq A\leq 36.\) If A is of the form \(A=9a^ 2\), these fields are related to the diophantine equation \[ x^ 3\quad +\quad y^ 3\quad +\quad z^ 3 = 3\quad. \] For a in the range \(1\leq a\leq 17\), the class numbers of these fields are also estimated (for \(a=1, 2, 3, 4\) the exact values are given). Reviewer: R.J.Stroeker MSC: 11R16 Cubic and quartic extensions 11R23 Iwasawa theory 11D25 Cubic and quartic Diophantine equations 12-04 Software, source code, etc. for problems pertaining to field theory Keywords:cubic diophantine equation; cubic fields; class numbers PDFBibTeX XMLCite \textit{M. Scarowsky} and \textit{A. Boyarsky}, Int. J. Math. Math. Sci. 9, 797--800 (1986; Zbl 0626.12005) Full Text: DOI EuDML