Rational L-function (awaiting review)

A rational L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes \[ L(s)=\prod_pL_p(p^{-s})^{-1} \] with $L_p\in \Z[T]$.