show · lfunction.zeros all knowls · up · search:

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.

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2019-05-18 08:49:23
Referred to by:
History: (expand/hide all) Differences (show/hide)