On the regularity of primes in arithmetic progressions

Christian Elsholtz, Niclas Technau, Robert Tichy

Published 2016-02-13Version 1

We prove that for a positive integer $k$ the primes in certain kinds of intervals can not distribute too 'uniformly' among the reduced residue classes modulo $k$. Hereby, we prove a generalization of a conjecture of Recaman and establish our results in a much more general situation, in particular for prime ideals in number fields.