On the digits of primes and polynomial sequences<br> <br>

Jo"el Rivat, Univ. Marseille <br> <br>

Abstract: <br>
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. <br>
  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.