@incollection{Martin2000,
author={G. Martin},
title={Asymmetries in the {S}hanks-{R}{\'e}nyi prime number race},
abstract={It has been well-observed that an inequality of the type $\pi(x;q,a) > \pi(x;q,b)$
is more likely to hold if $a$ is a non-square modulo $q$ and $b$ is a square
modulo $q$ (the so-called ``Chebyshev Bias''). For instance, each of $\pi(x;8,3)$,
$\pi(x;8,5)$, and $\pi(x;8,7)$ tends to be somewhat larger than $\pi(x;8,1)$.
However, it has come to light that the tendencies of these three $\pi(x;8,a)$
to dominate $\pi(x;8,1)$ have different strengths. A related phenomenon
is that the six possible inequalities of the form $\pi(x;8,a_1) > \pi(x;8,a_2)
> \pi(x;8,a_3)$ with {$a_1,a_2,a_3$}={3,5,7} are not all equally likely---some
orderings are preferred over others. In this paper we discuss these phenomena,
focusing on the moduli $q=8$ and $q=12$, and we explain why the observed
asymmetries (as opposed to other possible asymmetries) occur.},
booktitle={Number theory for the millennium, II (Urbana, IL, 2000)},
publisher={A K Peters},
year= 2002,
address={Natick, MA},
mrnumber={1 956 261},
note={\href{http://arxiv.org/abs/math/0010086}{Preprint}}
}
