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István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics

Chapter Chapter 16 in Diophantine Equations and Power Integral Bases, 2019, pp 273-311 from Springer

Abstract: Abstract At the end of the book we provide the reader with the results of our computations. Here we include those cases where we could make extensive computations. Recall that several examples are also given in the corresponding sections. In Sects. 16.1 and 16.2 we list the solutions of binomial Thue equations and binomial relative Thue equations, respectively. We made extensive computations in cubic, quartic, and sextic fields. The table of Sect. 16.3 gives all generators of power integral bases in about 130 cubic fields with small discriminants (both positive and negative). In Sect. 16.4 we provide a list of pure cubic fields. Section 16.5 is devoted to tables of quartic fields. We include tables that summarize the behavior of minimal indices of quartic fields as the discriminant grows. We consider cyclic quartic fields in Sect. 16.5.3. The complete lists of totally real and totally complex bicyclic biquadratic number fields up to discriminants 106 and 104, respectively, with all possible generators of power integral bases are given in Sects. 16.5.5 and 16.5.6, respectively. Monogenity data are given in a large number of further quartic fields in Sect. 16.5.7. The five totally real cyclic sextic fields with smallest discriminants are listed in Sect. 16.6.1 with all generators of power integral bases. The 25 sextic fields with an imaginary quadratic subfield with smallest discriminants (in absolute value) and their generators of power integral bases are given in Sect. 16.6.2. Section 16.7 contains the list of integral bases in the family of simplest sextic fields.

Date: 2019
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DOI: 10.1007/978-3-030-23865-0_16

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