The sum of digits of primes in $${\mathbb{Z}}$$[i]

We study the distribution of the complex sum-of-digits function s _q with basis q = –a±i, \({a \in \mathbb{Z}^+}\) for Gaussian primes p. Inspired by a recent result of Mauduit and Rivat (http://iml.univ-mrs.fr/~rivat/publications.html) for the real sum-of-digits function, we here get uniform distribution modulo 1 of the sequence (αs _q (p)) provided \({\alpha \in \mathbb{R} \setminus \mathbb{Q}}\) and q is prime with a ≥ 28. We also determine the order of magnitude of the number of Gaussian primes whose sum-of-digits evaluation lies in some fixed residue class mod m.