On the digits of primes and polynomial sequences

Jo"el Rivat, Univ. Marseille

In 1968, A.O. Gelfond conjectured that the sum of the digits of the primes is equidistributed in residue classes. He also conjectured the same result for the sum of the digits of appropriate polynomial sequences.
We will discuss the proof of these conjectures and some extensions and generalizations in recent joint works with Michael Drmota, Bruno Martin and Christian Mauduit.