Description:

In 1967, Gelfond established an asymptotic formula for the sum of digits of an integer n in base q in arithmetic progressions. In the paper, he posted a few questions about the distribution of sums of digits along special subsequences, such as primes and integer polynomials. The formula for primes was established in the famous work of Mauduit and Rivat (2010). Later, Drmota, Mauduit, and Rivat (2020) extended this result for sums of digits of primes in two different bases simultaneously. In the talk, we will discuss the proof for any number of bases and some connections to ergodic theory and automata. This is a joint work in progress with Clemens Müllner and Lukas Spiegelhofer.