engleski

Determining elements of minimal index in some parametric families of bicyclic biquadratic fields

In this talk, we will first present two different methods for determining monogenity and all elements of the minimal index in some infinite parametric families of totally real bicyclic biquadratic number fields. In certain parametric families, the problem is reduced the problem to the resolution of a system of Pellian equations. We will show how the theory of continued fractions can be used to determine the minimal index. In a joint work with István Gaál, we considered a similar type of family of number fields, but we applied a quite different technique, involving extensive formal and numerical calculations, as well. Also, in the present talk, we will deal with the issue of the existence of primitive integral elements having index divisible by fixed primes in one parametric family of bicyclic biquadratic fields. This problem comes down to the resolution p-adic analogue of the index form equations in a given family of biquadratic fields. In the last part of the talk, we will consider the problem of computing relative power integral bases in one family of quartic extensions of imaginary quadratic fields. We will recall the main result and briefly describe the proof. This is joint work with Zrinka Franušić.

minimal index, index form equation, bicyclic biquadratic fields, p-adic version of the index form equations, relative power integral bases, system of relative Pellian equations

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