Mathieu equation and Elliptic curve
arXiv:1006.5185 · doi:10.1088/0253-6102/58/6/08
Abstract
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 and , 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.
12 pages; minor improvement of the Conclusion section, references added