Mikael Passare showed how to compute [$\zeta(2)$](http://front.math.ucdavis.edu/0701.5039) using the [amoeba](http://www.ams.org/notices/200208/what-is.pdf) of $1 + z + w = 0$.  Was this ever generalized to higher zeta-values?  How might one compute $\zeta(2n)$ this way?

$$ \zeta(2) = \int_0^\infty \log(1 - e^x) \, dx = \frac{1}{3}\int_{s + t < \pi} 1 \; ds \, dt $$

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/0hecL.png