Generalization of Gelfond’s lemma on small values of integer polynomials to the multidimensional case

N. I. Kalosha ; Zh. I. Panteleeva

Trudy Instituta matematiki, Tome 32 (2024) no. 1, pp. 10-16.

Résumé

The paper establishes a relationship between the values of two integer polynomials without common roots on disjoint intervals of fixed length with the main characteristics of the polynomials – degree and height. The proved theorem can be considered as a two-dimensional generalization of Gelfond's lemma from the theory of transcendental numbers. The theorem can be used to estimate from above the Hausdorff dimension of a set of vectors that are approximated by conjugate algebraic numbers in a given order.

Détail

Mots-clés : diophantine approximation
Keywords: integral polynomial, algebraic numbers, Dirichlet’s theorem, reducible polynomials.

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