Нижняя оценка на арифметическую сложность слов Штурма

We give an $O(n^3)$ lower bound for the arithmetical complexity of a Sturmian word, that is the number of words of length $n$ occuring in all arithmetic progressions of a Sturmian word. This result supplements the recent $O(n^3)$ upper bound for the same function by Cassaigne and Frid.