As the title of the question suggests, what is the intuition behind Dirichlet's Class Number Formula being true? The Dirichlet Class Number Formula is$$h(\mathcal{O}_D) = -{1\over{D}} \sum_{n=1}^D n\left({{-D}\over{n}}\right)$$for $D > 4$, where $\left({{-D}\over{n}}\right)$ is the Kronecker symbol.


closed as primarily opinion-based by Will Jagy, user26857, Dietrich Burde, user223391, graydad Jul 19 '15 at 7:40

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    $\begingroup$ I don't know what you mean exactly by "intuition". An instructive special case is the imaginary quadratic case, see here. For a somewhat related MO question, see here. $\endgroup$ – Dietrich Burde Jul 17 '15 at 15:05
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    $\begingroup$ It is a rather elegant doublue-counting argument, but in my humble opinion it is far from being "trivial" or "intuitive". $\endgroup$ – Jack D'Aurizio Jul 17 '15 at 15:09
  • $\begingroup$ Duplicate? Intuition for Class Numbers $\endgroup$ – Jonas Meyer Jul 18 '15 at 2:00