Frequencies of successive tuples of Frobenius classes. (English) Zbl 1198.11081

Ash, Avner; Bate, Brandon; Gross, Robert

Exp. Math. 18, No. 1, 55-64 (2009).

The authors consider the sequence of Frobenius conjugacy classes for a Galois extension \(K/\mathbb{Q}\), ordered by the increasing sequence of rational primes. For a given \(K\) the authors look at the frequencies of nonoverlapping consecutive \(k\)-tuples in this sequence. These frequencies are compared with those expected by the Chebotarev density theorem, if there were statistical independence between successive Frobenius classes. The study is of an experimental nature and the findings are summarized as follows: When \(K\) contains an abelian extension (which may be \(K\) itself) with small absolute discriminant, one finds nonrandom behaviour. Otherwise one tends to see random behaviour.

Reviewer: Christian Elsholtz (Graz)

MSC:

11N05	Distribution of primes
11K45	Pseudo-random numbers; Monte Carlo methods
62P99	Applications of statistics

Keywords:

Frobenius classes; pseudorandom sequences