Problem on Miller's Primality test

Question

I am reading Miller's paper entitle "RIEMANN's HYPOTHESIS and Tests for Primality".

In the last page, it is defined Dirichlet's L function by $L(S,\chi)=\sum_{n=1}^{\infty} \chi(n)/n^s$ and $\chi(n)$ is defined by Legengre symbol $(\frac{n}{p})$. But what is $p$ here? Is it fixed prime?

Answer 1

Yes, for each prime $p$ there is a quadratic character $\chi_p$ and a corresponding $L$-function $L(s,\chi_P)=\sum\chi_p(n)n^{-s}$. If $p$ is understood from context, then you can do without the subscript $p$.