## Experimental Mathematics

- Experiment. Math.
- Volume 18, Issue 1 (2009), 55-64.

### Frequencies of Successive Tuples of Frobenius Classes

Avner Ash, Brandon Bate, and Robert Gross

#### 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.

#### Article information

**Source**

Experiment. Math., Volume 18, Issue 1 (2009), 55-64.

**Dates**

First available in Project Euclid: 27 May 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1243430529

**Mathematical Reviews number (MathSciNet)**

MR2548986

**Zentralblatt MATH identifier**

1198.11081

**Subjects**

Primary: 11N05: Distribution of primes 11K45: Pseudo-random numbers; Monte Carlo methods 62P99: None of the above, but in this section

**Keywords**

Frobenius classes, pseudorandom sequences

#### Citation

Ash, Avner; Bate, Brandon; Gross, Robert. Frequencies of Successive Tuples of Frobenius Classes. Experiment. Math. 18 (2009), no. 1, 55--64. https://projecteuclid.org/euclid.em/1243430529