Geodesic
Polynomials generating maximal real subfields of circular fields
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 469-481

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We have constructed recurrence formulas for polynomials $q_n(x)\in\mathbb Q[x]$, any root of which generates the maximal real subfield of circular field $K_{2n}$. It has been shown that all real subfields of fixed field $K_{2n}$ can be described by using polynomial $q_n(x)$ and its Galois group. Furthermore, a methodology has been developed for presentation of square radical $\sqrt d$, $d\in\mathbb N$, $d>1$ in the form of a polynomial with rational coefficients relative to $2\cos(\pi/n)$ at the corresponding $n$. The theoretical results have been verified by a number of examples.
Keywords: algebraic number, circular fields and their subfields
Mots-clés : minimal polynomial, Galois group. 
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     author = {I. G. Galyautdinov and E. E. Lavrentyeva},
     title = {Polynomials generating maximal real subfields of circular fields},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     volume = {158},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a1/}
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I. G. Galyautdinov; E. E. Lavrentyeva. Polynomials generating maximal real subfields of circular fields. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 469-481. http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a1/