Generalization of Gelfond’s lemma on small values of integer polynomials to the multidimensional case
Abstract
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.
About the Authors
N. I. Kalosha
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
Zh. I. Panteleeva
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
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Review
For citations:
Kalosha N.I., Panteleeva Zh.I. Generalization of Gelfond’s lemma on small values of integer polynomials to the multidimensional case. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2024;32(1):10-16. (In Russ.)
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