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:**

- intro.features
- intro.tutorial
- lfunction
- lfunction.trivial_zero
- rcs.cande.lfunction
- rcs.rigor.lfunction.curve
- rcs.rigor.lfunction.dirichlet
- rcs.rigor.lfunction.ec
- rcs.rigor.lfunction.lcalc
- rcs.rigor.lfunction.modular
- lmfdb/lfunctions/main.py (line 389)
- lmfdb/lfunctions/templates/LfunctionSearchResults.html (line 31)

**History:**(expand/hide all)

- 2019-05-18 08:49:23 by Andrew Sutherland (Reviewed)
- 2019-05-14 07:47:53 by David Farmer
- 2019-05-14 06:39:43 by Andrew Sutherland
- 2019-05-11 15:51:17 by Andrew Sutherland (Reviewed)
- 2012-03-28 03:10:56 by Alina Bucur (Reviewed)

**Differences**(show/hide)