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.