Polynomials Generating Maximal Real Subfields of Circular Fields
We have constructed recurrence formulas for polynomials qn(x) ɕ Q[x], any root of which generates the maximal real subfield of circular field K2n. It has been shown that all real subfields of fixed field K2n can be described by using polynomial qn(x) and its Galois group. Furthermore, a methodology...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2016-12-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | http://kpfu.ru/portal/docs/F1697277406/158_4_phys_mat_2.pdf |
| _version_ | 1797964968001273856 |
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| author | I.G. Galyautdinov E.E. Lavrentyeva |
| author_facet | I.G. Galyautdinov E.E. Lavrentyeva |
| author_sort | I.G. Galyautdinov |
| collection | DOAJ |
| description | We have constructed recurrence formulas for polynomials qn(x) ɕ Q[x], any root of which generates the maximal real subfield of circular field K2n. It has been shown that all real subfields of fixed field K2n can be described by using polynomial qn(x) and its Galois group. Furthermore, a methodology has been developed for presentation of square radical d1/2, d ɕ N, d > 1 in the form of a polynomial with rational coefficients relative to 2cos(π/n) at the corresponding n. The theoretical results have been verified by a number of examples. |
| first_indexed | 2024-04-11T01:52:53Z |
| format | Article |
| id | doaj.art-3c041c0bc6a34281919bc750ac15d2ba |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-11T01:52:53Z |
| publishDate | 2016-12-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-3c041c0bc6a34281919bc750ac15d2ba2023-01-03T06:01:45ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982016-12-011584469481Polynomials Generating Maximal Real Subfields of Circular FieldsI.G. Galyautdinov0E.E. Lavrentyeva1Volga State University of Telecommunications and Informatics, Kazan Branch, Kazan, 420061 Russia Kazan Federal University, Kazan, 420008 RussiaWe have constructed recurrence formulas for polynomials qn(x) ɕ Q[x], any root of which generates the maximal real subfield of circular field K2n. It has been shown that all real subfields of fixed field K2n can be described by using polynomial qn(x) and its Galois group. Furthermore, a methodology has been developed for presentation of square radical d1/2, d ɕ N, d > 1 in the form of a polynomial with rational coefficients relative to 2cos(π/n) at the corresponding n. The theoretical results have been verified by a number of examples.http://kpfu.ru/portal/docs/F1697277406/158_4_phys_mat_2.pdfalgebraic numberminimal polynomialcircular fields and their subfieldsGalois group |
| spellingShingle | I.G. Galyautdinov E.E. Lavrentyeva Polynomials Generating Maximal Real Subfields of Circular Fields Учёные записки Казанского университета. Серия Физико-математические науки algebraic number minimal polynomial circular fields and their subfields Galois group |
| title | Polynomials Generating Maximal Real Subfields of Circular Fields |
| title_full | Polynomials Generating Maximal Real Subfields of Circular Fields |
| title_fullStr | Polynomials Generating Maximal Real Subfields of Circular Fields |
| title_full_unstemmed | Polynomials Generating Maximal Real Subfields of Circular Fields |
| title_short | Polynomials Generating Maximal Real Subfields of Circular Fields |
| title_sort | polynomials generating maximal real subfields of circular fields |
| topic | algebraic number minimal polynomial circular fields and their subfields Galois group |
| url | http://kpfu.ru/portal/docs/F1697277406/158_4_phys_mat_2.pdf |
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