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Dirichlet Structure Constant


\begin{displaymath}
\kappa(d)=\cases{
{2\ln\eta(d)\over\sqrt{d}} & for $d>0$\cr
{2\pi\over w(d)\sqrt{\vert d\vert}} & for $d<0$,\cr}
\end{displaymath}

where $\eta(d)$ is the Fundamental Unit and $w(d)$ is the number of substitutions which leave the binary quadratic form unchanged

\begin{displaymath}
w(d)=\cases{
6 & for $d=-3$\cr
4 & for $d=-4$\cr
2 & otherwise.\cr}
\end{displaymath}

See also Class Number, Dirichlet L-Series


References

mathematica.gif Weisstein, E. W. ``Class Numbers.'' Mathematica notebook ClassNumbers.m.




© 1996-9 Eric W. Weisstein
1999-05-24