Frequencies of Successive Tuples of Frobenius Classes

Abstract

In this paper, we consider the sequence of Frobenius conjugacy classes for a Galois extension $K/\QQ$, ordered by the increasing sequence of rational primes. For a given $K$, we look at the frequencies of nonoverlapping consecutive $k$-tuples in this sequence. We compare these frequencies to what would be expected by the Cebotarev density theorem if there were statistical independence between successive Frobenius classes. We find striking variations of behavior as $K$ varies.