On the digits of shifted primes (Q481389)

In recent years much progress has been obtained concerning our understanding of the distribution of digital functions evaluated on sparse sequences, such as the primes. In the present paper, the authors extend recent work on digital functions evaluated at prime arguments due to \textit{B. Martin}, \textit{C. Mauduit} and \textit{J. Rivat} [Acta Arith. 165, No. 1, 11--45 (2014; Zbl 1395.11023), Acta Arith. 170, No. 2, 175--197 (2015; Zbl 1395.11024).] to the case of shifted primes. Their main result is a non-trivial estimate of the exponential sum \(\sum_{n<x} \Lambda(n) e(f(n+c_n)+\beta n)\) where \(\Lambda\) denotes the von Mangoldt function, \(f\) is a digital function satisfying a certain non-degeneracy property, \(\beta\) is any real number and \((c_n)\) is an almost-periodic integer-valued sequence. Besides precise statistical information, the authors obtain (as in the paper of Martin, Mauduit, Rivat) results for the ternary Goldbach problem where the shifts of the three primes satisfy congruence conditions on their digits.