2010

Mathieu equation and Elliptic curve

He, Wei, Miao, Yan-Gang

Understand

We present a relation between the Mathieu equation and a particular elliptic curve.

We find that the Floquet exponent of the Mathieu equation, for both $q<<1$ and $q>>1$, can be obtained from the integral of a differential one form along the two homology cycles of the elliptic curve.
Certain higher order differential operators are needed to generate the WKB expansion.
We provide a fifth order proof.

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