Andrei Shubin: Prime number theorem for sums of digits in several bases

Abstract:

 In 1967, Gelfond established an asymptotic formula for the sum of digits of an integer \(n\) in base \(q\) in arithmetic progressions. He conjectured similar formulas for the sums of digits of primes and integer polynomials. The case of primes was completely resolved 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 this talk, we will describe the proof for any number of bases. We will also discuss the connection of these results to ergodic theory and automata.

This is a joint work in progress with Clemens Müllner.