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arXiv · 1708.04288

Primitive root biases for prime pairs I: existence and non-totality of biases

Stephan Ramon Garcia·Florian Luca·Timothy Schaaff
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Abstract

We study the difference between the number of primitive roots modulo $p$ and modulo $p+k$ for prime pairs $p,p+k$. Assuming the Bateman-Horn conjecture, we prove the existence of strong sign biases for such pairs. More importantly, we prove that for a small positive proportion of prime pairs $p,p+k$, the dominant inequality is reversed.

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Stephan Ramon Garcia, Florian Luca, Timothy Schaaff. 2017-08-14. Primitive root biases for prime pairs I: existence and non-totality of biases. https://arxiv.org/abs/1708.04288

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