The Zsiflaw--Legeis theorem for arbitrary bases

In this paper, we prove analogues of the Dirichlet theorem on arithmetic progressions and the Siegel–Walfisz theorem for the digital reverses of primes for arbitrary bases, which the authors obtained in the previous paper but only for large bases. The proof is based on a generalization of the result of Martin–Mauduit–Rivat (2014) on the exponential sums over primes with the so-called ``digital’’ functions.