Experimental Mathematics

Frequencies of Successive Tuples of Frobenius Classes

Avner Ash, Brandon Bate, and Robert Gross

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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


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