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Corrigendum to “On density modulo 1 of some expressions containing algebraic integers”. (English) Zbl 1202.11041
Let \(\lambda_1,\mu_1\) and \(\lambda_2,\mu_2\) be two distinct pairs of multiplicatively independent real algebraic integers of degree 2 and let \(\xi_1,\xi_2\) be a pair of real numbers which are not both equal zero. In series of papers the author studies everywhere density of the double sequence \(\lambda_1^n\mu_1^m\xi_1+\lambda_2^n\mu_2^m\xi_2\bmod1\), \(m,n=1,2,\dots\) in \([0,1)\). In this Corrigendum he notes that his assumptions on \(\lambda_1,\mu_1,\lambda_2,\mu_2\) given in [Acta Arith. 127, 217–229 (2007; Zbl 1118.11034)] does not imply the density modulo 1 of \(\lambda_1^n\mu_1^m\xi_1+\lambda_2^n\mu_2^m\xi_2\) for any \(\xi_1,\xi_2\), but only for given \(\xi_1,\xi_2\) there exists a natural number \(\kappa\) such that \(\lambda_1^n\mu_1^m\kappa\xi_1+\lambda_2^n\mu_2^m\kappa\xi_2\bmod1\) is everywhere dense in \([0,1]\).

MSC:
11K31 Special sequences
11J71 Distribution modulo one
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