| Title |
Linear relations of four conjugates of an algebraic number |
| Authors |
Baronėnas, Žygimantas ; Drungilas, Paulius ; Jankauskas, Jonas |
| DOI |
10.4153/S0008439525101148 |
| Full Text |
|
| Is Part of |
Canadian mathematical bulletin.. Cambridge : Cambridge University Press on behalf of Canadian Mathematical Society. 2025, Early Access, p. [1-16].. ISSN 0008-4395. eISSN 1496-4287 |
| Keywords [eng] |
algebraic numbers ; linear relations in algebraic conjugates ; algebraic conjugates |
| Abstract [eng] |
We characterize all algebraic numbers α of degree d ∈ {4, 5, 6, 7} for which there exist four distinct algebraic conjugates α1, α2, α3, α4 of α satisfying the relation α1 + α2 = α3 + α4. In particular, we prove that an algebraic number α of degree 6 satisfies this relation with α1 + α2 /∈ Q if and only if α is the sum of a quadratic and a cubic algebraic number. Moreover, we describe all possible Galois groups of the normal closure of Q(α) for such algebraic numbers α. We also consider similar relations α1 + α2 + α3 + α4 = 0 and α1 + α2 + α3 = α4 for algebraic numbers of degree up to 7. |
| Published |
Cambridge : Cambridge University Press on behalf of Canadian Mathematical Society |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
