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The minimum discriminant of totally real algebraic number fields of degree $ 9$ with cubic subfields


Author: Hiroyuki Fujita
Journal: Math. Comp. 60 (1993), 801-810
MSC: Primary 11R16; Secondary 11R29, 11R80, 11Y40
MathSciNet review: 1176709
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Abstract: With the help of the computer language UBASIC86, the minimum discriminant $ d(K)$ of totally real algebraic number fields K of degree 9 with cubic subfields F is determined. It is given by $ d(K) = 16240385609$. The defining equation for K is given by $ f(x) = {x^9} - {x^8} - 9{x^7} + 4{x^6} + 26{x^5} - 2{x^4} - 25{x^3} - {x^2} + 7x + 1$, and K is uniquely determined by $ d(K)$ up to Q-isomorphism. The field K has the cubic subfield F with $ d(F) = 49$ defined by the polynomial $ f(x) = {x^3} + {x^2} - 2x - 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1176709-6
Article copyright: © Copyright 1993 American Mathematical Society