Type: Article
Publication Date: 2010-04-25
Citations: 147
DOI: https://doi.org/10.4007/annals.2010.171.1591
In this article we answer a question proposed by Gelfond in 1968.We prove that the sum of digits of prime numbers written in a basis q > 2 is equidistributed in arithmetic progressions (except for some well known degenerate cases).We prove also that the sequence .˛sq .p//where p runs through the prime numbers is equidistributed modulo 1 if and only if ˛2 ޒ n .