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.
- Review status: reviewed
- Last edited by David Roberts on 2019-05-03 20:34:04
Not referenced anywhere at the moment.
- 2019-05-03 20:34:04 by David Roberts (Reviewed)
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