Return to Revisions

For any function $f$ holomorphic on some domain $D$, the integral $$ \frac{1}{2\pi i} \int_{\partial D} \frac{df}{f} $$ is a nonnegative integer, and counts the number of zeros of $f$ in $D$. So if you can compute this integral to good enough precision, you know the exact number of zeroes in $D$. By taking $D$ a small enough disc around a suspected zero, you have a proof that there is actually a zero there.