Zeros of an L-function (reviewed)

The zeros of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.

Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization).

The lowest zero of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.