Petits discriminants des corps de nombres totalement imaginaires de degré 8

AbstractIn this paper we show that there are, up to isomorphisms, exactly 15 totally imaginary eight-degree number fields having a discriminant smaller than 1656110. The proof of this result was obtained in the following manner: For each totally imaginary eight-degree number field with a discriminant smaller than 1656110, we constructed a polynomial, one root of which was a generator of the number field. In order to circumscribe the number of polynomials to be studied, we used, on the one hand, methods issuing from the geometry of numbers and on the other, the method developed by Odlyzko, Poitou, and Serre for the determination of lower bounds for discriminants