Fairmont Le Reine Elizabeth (Montréal), 7 - 10 décembre 2012
Rubinstein and Sarnak proved conditionally that every prime number race is inclusive; they assumed not only the generalized Riemann hypothesis but also a strong statement about the linear independence of the zeros of Dirichlet $L$-functions. On the other hand, Ford and Konyagin showed that prime number races could fail to be inclusive if the generalized Riemann hypothesis is false. We will discuss these results, as well as some work in progress with Nathan Ng where we substantially weaken the second hypothesis used by Rubinstein and Sarnak.
This is joint work with Eric Landquist (Kutztown University, Pennsylvania) and
Andreas Stein (University of Oldenburg, Germany).