Additive and multiplicative relations connecting conjugate algebraic numbers

DOI10.1016/0022-314X(86)90094-6zbMath0586.12001OpenAlexW2042904939MaRDI QIDQ1071801

Christopher J. Smyth

Publication date: 1986

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(86)90094-6

zbMATH Keywords

Galois groupsequationsincomplete Latin squareconjugate algebraic integers

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative and norm form equations (11D57)

Related Items (13)

Mahler measure on Galois extensions ⋮ Linear relations among Galois conjugates over \(\mathbb{F}_q(t)\) ⋮ Ultra-short sums of trace functions ⋮ Linear relations with conjugates of a Salem number ⋮ Testing degenerate polynomials ⋮ A fast algorithm for computing multiplicative relations between the roots of a generic polynomial ⋮ On the number of integer polynomials with multiplicatively dependent roots ⋮ A degree problem for two algebraic numbers and their sum ⋮ Additive Hilbert's theorem 90 in the ring of algebraic integers ⋮ The values of Mahler measures ⋮ A degree problem for the compositum of two number fields ⋮ On the behavior of Mahler's measure under iteration ⋮ An effective version of the primitive element theorem

Cites Work

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• New light on Frobenius' creation of the theory of group characters
• The origin of the theory of group characters
• On a question of Lehmer and the number of irreducible factors of a polynomial
• Conjugate algebraic numbers on conics

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