Normality of some decimals generated by primes in a residue class (Q1938562)

In the article under review, the authors construct normal numbers by using the sequence of primes in residue classes. This involves exponential sum estimates of various kinds. We call that a real number is normal (with respect to base \(q\)) if in its \(q\)-ary expansion every block of \(k\) digits occurs with the expected asymptotic frequency \(q^{-k}\). Their main result shows that if \(f\) is a polynomial of degree \(\geq1\) with real coefficients but with leading coefficient a rational number or \(f\) is a transcendental entire function having logarithmic order \(\alpha\) with \(1\leq\alpha<4/3\), then the number \[ 0.[f(p_1)]_q[f(p_2)]_qf(p_3)]_q\ldots, \] where \([\cdot]_q\) denotes the \(q\)-ary expansion and \((p_i)_{i\geq1}\) is the sequence of primes \(\equiv\ell\bmod k\), is normal in base \(q\).