This is a brief post to record a cool trick from a talk by Vladimir Dokchitser today at the BSD conference.

In computing the parity of the analytic rank of an elliptic curve he used the following trick. Observe that if f(x) = f(-x) for f an analytic function then f is even, so has an even order of vanishing at x=0. Conversely, if f(x)=-f(-x), it has an odd order of vanishing at x=0. So weirdly, by computing whether a function is odd or even, one can seem to determine the parity of its order of vanishing.