Biases in the prime number race of function fields
Let \(\pi(a,m,N)=\#\{ P\mid P\equiv a\bmod m,\,\deg(P)=N\}\). In this paper, the main theorem gives an explicit description of the density \(\delta_{m;a_{1},\dots,a_{r}}\) of the subset \(\{X\in \mathbb{Z}\mid X>0,\sum_{N=1}^{X}\pi(a_{1},m,N)>\dots>\sum_{N=1}^{X}\pi(a_{r},m,N)\}\) of all positive integers in terms of the measure \(\mu(\{(x_1,\dots,x_r \in\mathbb{R}^{r}\mid x_1>\dots>x_r)\})\). This is a function field analog of the work of \textit{A. Feuerverger} and \textit{G. Martin} [Exp. Math. 9, No. 4, 535--570 (2000; Zbl 0976.11041)], who established such formula in the number field case, building up on the fundamental work of \textit{M. Rubinstein} and \textit{P. Sarnak} [Exp. Math. 3, 173--197 (1994; Zbl 0823.11050)].
scientific article; zbMATH DE number 5690737