For each positive integer $n$, let $C_n$ for the minimum root discriminant for all number fields of degree $n$. Assuming the Generalized Riemann Hypothesis, $\limsup C_n \geq \Omega$ where
$$ \Omega = 8\pi e^\gamma\approx 44.7632\ldots$$
and $\gamma$ is the Euler–Mascheroni constant. Lower bounds for the $C_n$ were deduced by analytic methods through the work of Odlyzko and others. In particular, Serre introduced the constant $\Omega$ which we refer to as the **Serre Odlyzko bound**,

Consequently, any number field whose root discriminant lies below $\Omega$ can be considered to have small discriminant.

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**Knowl status:**

- Review status: reviewed
- Last edited by David Roberts on 2019-05-03 20:34:04

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

- 2019-05-03 20:34:04 by David Roberts (Reviewed)
- 2019-05-03 19:01:32 by John Jones
- 2019-03-20 14:57:58 by John Jones
- 2019-03-20 14:54:39 by John Jones
- 2019-03-20 14:53:17 by John Jones
- 2019-03-20 14:49:37 by John Jones
- 2019-03-20 14:48:14 by John Jones
- 2019-03-20 14:47:49 by John Jones
- 2019-03-20 14:46:51 by John Jones
- 2019-03-20 14:46:05 by John Jones

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