Distribution of the values of \(q\)-additive functions on polynomial sequences (Q1897514)

Let \(f\) be a \(q\)-additive function and \(P\) a polynomial with integer coefficients. The authors show that under some conditions the frequencies of \(f\circ P\) converge to the normal distribution function. They use theorems of Vinogradov and Hua for trigonometric sums and of Erdös and Turán for the discrepancy of sequences mod 1.