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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
##### Keywords:
density modulo 1; algebraic number
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