Mathieu equation and Elliptic curve

Details Mathieu equation and Elliptic curve Mathieu equation and Elliptic curve

2010-06-27

arxiv.org/abs/1006.5185v3

Physics

Mathematical Physics

12 pages; minor improvement of the Conclusion section, references added

Scientific paper

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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